There's a locally-owned rental outfit that I use when I need a car or truck. Like the national chains, they'll come pick you up if you call them. If I'm on my bike when I pick up a car from them, they'll either stash it in their tool storage area or let me put it in the back seat of their car; I bring along a bed sheet to protect the interior from grease, and they know I've always taken good care of their cars.
If I have to rent from a corporate chain and I arrive by bike, I'll park it around the corner so they don't have to watch me load the bike into their car. Again, I just bring along a bedsheet in the panniers to protect the upholstery.
Having said all that, I've found that I need to rent a car a lot less often than I expected to when I first got rid of my own car. Maybe twice a year, usually to move heavy equipment like you mentioned.