This is likely because the painting company subs this out to siding guys, or they have their own siders and can get more business by providing turnkey renovations of this sort. It's easier for customers to deal with one company than to find separate siders and painters, and it makes it easier for you if you end up with problems afterward, since the same contractor did the whole job.

With that said, and this is where I hope you get some pros to respond, I am unsure if a carpentry license is even required for doing wood siding. (and I'm sure this varies by state, country, etc.)

You should ask the painting company this question. I don't think that normal painters will do this, but they could be one of those full service type companies too.

Shingles should really be done by someone with experience, not someone who has done a few. I would find a siding company with shingle experience and used prestained shingles. There are a lot of houses around here that are shingled. They are usually only painted (rather than stained) when the shingles are old and not great looking.