I would have laughed

. Thats weird. The question from him was kinda weird too...guess he was wanting to do the job for cash to keep it off the books? Or worked for a big company and was willing to cut you a deal if you paid cash and come do it on the weekend as a side job? The 2nd practice is unethical...he is "cutting the throat" of the garage door company who employs him to put more money in his own pocket in that circumstance but I have seen guys do it. Garage door installation here in Charlotte is dominated by a big company called Overhead Door. They are fast and good at what they do though.
I thought your joke was hilarious btw..
Edit: or the guy/company has a policy of being paid before the work is performed rather than after? Guess it depends on whether he was there to install the door which is what I thought...if he just came out to measure the door rather than you just telling them your Finished RO for the door then it wouldn't be weird for them to take a deposit I guess before ordering the door if for some reason you have a special RO that has to be ordered etc. The vast majority of doors are All the same standard sizes in residential buildings though and this is highly unlikely to not be a standard door width and height. Assuming the door is standard sized, deposits arent normally required because if you change your mind and go with someone else they will just install the door in someone elses house because they keep a big inventory of standard doors anyway.