I would hope that the company is legit enough to send out people who can look at a roof and determine if there is hail damage, and if not, don't disturb the resident.
The one in the Heights that I have mentioned earlier gave a senior citizen discount of 20% if paid in full in cash BEFORE work started. As it turned out he had a lot of takers around Illinois.
I am comfortable with 1/3 down if I know the contractor, but would hesitate with someone new unless I had good references from friends. I have had a lot of cold calls lately saying that "so & so" would be in the area and checking roofs & gutters and want to look at mine. I decline or hang up.
I would always ask for money on parts and materials needed to do the Job. 20 years of doing bodywork and painting never had a problem. Insurance claims are different. I remember having to wait 90 days for checks to clear.