I've got a F&P single door bottom freezer fridge. Mine is in a 36" cabinet opening with cabinets on one side and a side panel on the other. The doors sit proud of the cabinet opening -- the fridge body is cabinet depth, the doors are in front -- and we have no trouble accessing the bins.

Our model is the one with the freezer door with pullout shelves behind it, not the one where the whole freezer pulls out as one big drawer. I checked, and our freezer shelves can be pulled out with the freezer door opened 90 degrees. The fridge door, however, needs to be opened a bit farther to allow the produce bins to pull all the way out, because the door shelves get in the way if the door is at 90 degrees. You can open the bins and access the contents with the door at 90 degrees, but you can pull them out an extra inch or two if you open the door to more like 110-120 degrees.

Just another note on organization. If you are getting one without a deli drawer, like ours, and decide you want a drawer, the Container Store regular size shoe drawers fit great inside this fridge. (Most fridge bins are too long front-to-back for a counter-depth fridge.) It took me a while to find something that would work, so I thought I'd share. The link is below.

And just in case you're getting the same model with the freezer door that we have, the bottom "shelf" is a deep bin. I had the hardest time finding something to organize that thing, but it turned out that IKEA Kusiner boxes (in children's storage) fit perfectly, 3 in a row side by side:

http://www.ikea.com/us/en/catalog/products/20163265

(Sorry, I've tried about 10 ways to make that a clickable link but none of the codes I've tried work on this forum, and I can't find the instructions quickly.)

Here is a link that might be useful: Container Store clear shoe drawer

Thank you so much for your detailed response! If I were in a jam for space to open a crisper drawer, are the door shelves removable?

They are indeed, though the part they hook onto sticks out a bit and could impede the bins a little. You'd still be able to get into them with no trouble.

If worse comes to worst, you could scoot your fridge to one side of your 36" opening instead of centering it, and that would give you a couple more inches of leeway on the hinge side.