Fertilizing a KBG lawn in the heat of the summer is a prblem, especially in the dry intermountain west.

In my opinion, you were watering too frequently, unless the sod was brand new, in which case every other day is okay, but you could probably have watered for a shorter time. Howver, I don't think you were watering enough to cause a fungus issue.

Personally, I don't think what they're telling you makes much sense. They're telling you that it is drought stressed and needs more water, but that there is also fungus. Fungus is caused by too much water, not by too little.

It's unlikely that you'll get the lawn "service" company to admit that they made a mistake, but you can probably get them to charge you for additional services that will either do no good or will do more harm.

If you've got any green left in the lawn at all, I'd try to resurrect what you have. Cut back to watering every third day. Let the soil dry out to a depth of about 4 inches before watering again. If you have extremely sandy soil, you may need to water more often. Don't fertilize again until after the heat breaks, then fertilize once in early fall and once after the top growth has stopped but while the grass is still green. If you want, you can fertilize once next year late spring, but the fall schedule is far more important.

Do you see any of the insects they're telling you that you have? Did you hire the lawn company based on recommendations from somebody with a great lawn who said they're using them, or because they came by and left a flyer on your door? I had a lawn company stop their truck in front of my house and start pulling up patches of grass in an area where the sprinkler head had died, then tell me that it was caused by grubs. They clearly had no idea what they were talking about, but would gladly have charged me for grub treatment. I actually had to threaten to call the police and then get on the phone and start dialing before they'd leave. I've never seen any indication of grubs, before that visit or since.

Hot and dry does not equal fungus or disease. Hot and moist does. You may very well have some disease. You may very well have surface feeding insects. This does not explain their diagnosis and treatment. If you have "drought stress" and "mites and other insects", why did they not treat the problem they diagnosed? Instead they fertilized and applied an herbicide for insects and stress? If it is fungus or disease, they will not have anything to help anyway. Cancel their service, read here often, and become your own lawn professional.

Home, with the use of bluegrass as the sole type your lawn is made up of, then you have to accept what deficiencies such grass type has including how it stands up to summer heat and sun.

Kentucky Bluegrass goes dormant for a time, up to 3 weeks, in summer.
A better lawn has a combination of K.B. with a 40% mix of ryegrass and 20% creeping red fescue.
Each then can give its best...in shade as well as in sun.

Watering every other day...how's one to tell if this is needed unless one can measure how much is given at a time.
Rain notwithstanding, one inch per week is agreed to be sufficient to feed a lawn.
Too much, or too little, can cause grass roots to grow stubby, and not go deep where the moisture is necessary to be held onto.

Fertilizer. What sort of fertilizer was given the lawn and how much was applied.
The mention that the lawn blades are deep green does suggest the application was with a high nitrogen content.
This type is generally given in early spring and at times throughout the season.
But it is not prescribed for mid summer during the heat of summer when, pushed to grow, is soon starved of water, and goes brown.
Fertilizer with such nitrogen is best given at cooler periods when the grass is encouraged to grow and when it will survive the heat when it returns.

The sprinklers must have some indication of how much it/they deliver per minute of operation.
Forty minutes.....how much is given to the lawn.
The time of operation is important. Too early in the day, might bring about mildew and/or fungus problems.
Too late, as going into late evening wet, might bring about the same result.
So operating the system during the morning hours and late afternoon/early evening should allow the heat of day to dry the surface blades.

The color of the grass can, besides indicating a feeding of nitrogen, can also bring about a thatch problem.
Nitrogen is the culprit. If a lawn was heavy in thatch, less moisture is taken into the soil due to such barrier.
A good stiff raking might remove surface thatch that may be preventing proper amount of water being absorbed when it is wished to be absorbed.

You might look into how much fertilizer is given and how much nitrogen the bag contains and does it also contain sufficient phosphurus and potash levels.

One note: If this is a "NEW" homesite...i.e. new construction and not a re-sale, then you have to accept the builder did not leave your lawn with a good sub-soil and your lawn is growing its best with what conditions it was given. If you were to dig under the lawn, you might find buried bricks, mortar, and other building materials.

To be aware of what your soil's condition is would have to be proven by obtaining a soil test.
You might ask around, usually State-controlled, state funded colleges, have an extension service that provides such soil tests. If not there, then private laboratories do such tests.

It is not unusual though for homesites to have lousy topsoil--maybe brought in from the parking lot around the corner.
A program of topping up your lawn in spring as well as in the fall can prove very beneficial to your lawn.
A 1" topping of topsoil/triple mix/compost/sand/loam....in the fall and then do an overseeding of a good grass seed will give you a more lush growth.
Repeat this in early spring, letting the grass grow up through it.

To find out how much topsoil you might require is a simple method: measure the intended area's length, in feet; measure the intended area's width, in feet.

Multiply this by the depth of soil...in inches. (1" is good)
Then divide this by 1000 (move the decimal 3 points to the left) and multiply by 3.

This resulting figure gives you exactly the number of cubic yards needed to do the topping.

This overtopping of soil is recommended to be repeated year after year---at least for 4 consecutive years and an overseeding of a GOOD lawn seed be given.
This brings about a lush lawn, one that is able to stand up to adversity best.

If I were you, I would avoid rye in Denver. It won't make it through the summer. Denver's summers are too hot and dry for rye to make it.

Creeping red fescue will do fine in the shade, but will suffer in the sunny areas when it's hot out. If you have lots of shade, you can seed some creeping red fescue to those areas.

If you water properly, you can keep the KBG green all summer. KBG will also handle shade better in the Rockies than in most areas because the sunlight is filtered less due to the high altitude.

I wouldn't add an inch of topsoil a year for 4 years unless your soil is 4 inches below the sidewalk and driveway. If your soil is at the correct level now, adding 4 inches of topsoil will cause you plenty of problems down the road.

If you want to topdress your lawn to improve the soil, I'd use compost or other organic amendments. They'll help the soil, but since they decompose, they won't raise the depth of the soil.