your assumption is correct. Avis often issues contracts hours in advance for those set up to do so. The pickup time (its been years, so forgive me) is usually the time you requested it, or if you inputted a flight number, 30-50 (somewhere around there) minutes after your fight is scheduled to land. now if your airport has the automated system set up, it spits out the contracts when your flight ACTUALLY lands. all airports have it, but only the busiest use that system.

When on a preprinted contract, its always advisable to do a reality check of when the contract stipulates your pickup time is. Granted, knowledgeable agents can correct it for you on the spot, but usually you have to bring it to their attention. Also, the gate guards provide (at some airports) positive logging of your actual time you drive off the lot, but it still ends up being a manual process to update the pickup time. The last time I used avis (avis not budget) was in Hawaii. I flew into HNL and they had an agent in the parking lot who hand wrote the time on the stub end of the preprinted contract. I noticed the time (as I always do) and saw the time updated to the minute on my checkout printout. so I know that some places take this stuff seriously.

But once again, this can work against you as IAH traveler pointed out, so its a good thing to be acquainted with whatever coupon and your current booked rate, esp when dealing with flight delays which make you cross the two "barriers". The barriers are midnight and noon. If flight delays cause you to pick up after midnight, pay attention, as well as outbound delays cause you to return it after noon when you are on a coupon and scheduled by reservation to return before noon.

Having worked for a rental car company, i read every last detail on the most important stuff on every contract. pick up time, drop off time, daily rate, hourly rate, weekly rate if applicable, and the fine print on all coupons.