So did you get a late fee or something?
We have always rented a car for specific times and yes even through Costco.
If you reserved your car from noon until noon you still only have until noon the date of your reservation. Just because you picked up the car at 1:30pm does not change your reservation to 1:30pm the next day. Some companies offer grace periods; for Budget that is 29 mins and at 30 mins they can (although I'm not sure they always will) apply a late fee.
We have tons of experience with rental cars..my husband literally gets one all the time for work (including one earlier this week). Hundreds of rental cars over the years. You get your rental car for the time of your reservation no longer unless you want a fee to apply if it is applicable. You can alter your reservation to later depending on the company and the process is dependent on the company.
I'm not discounting you may have not experienced any pushback elsewhere but it is very standard that regardless of whether you picked the car up at your exact time you only have until the reservation end time to return it without modifying the existing reservation. In the world of rental cars this is really needed to keep reservations going. Imagine reserving a rental car and it's not available to you because someone always thought if they picked it up late their reservation just rolls on by. It has the potential to a domino effect on availability of cars for other people.
In particular to Budget
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As far as not getting the car you want I totally get the frustration on that. It varies between the companies and locations on what they have. I would however have expected a partial refund for the cost difference assuming their was one to get a downgrade from a standard SUV to an intermediate but there is not always a cost difference and we've checked Costco recently enough (in January) and sometimes the pricing is more sometimes it's less. I can imagine booking through Costco makes things a tad complicated as they negotiate deals with them to offer. When we were in Puerto Rico we rented through
Avis but they gave us technically a car in Budget's area. However, admittedly in Puerto Rico many of their cars had pre-existing damage so not sure they would have been nitpicky anyhow.