Hertz can put comments on your record, which in theory are read by the staff when allocating cars. About a year ago they added a comment to mine saying that I didn't like Nissan Sentras, and overnight I went from getting Sentras about half to time to never receiving one again, so it does seem to work.

For me this was added at an airport location, but I'm guessing anywhere (including over the phone) could add a comment saying that you want the type of car you reserved and nothing bigger.

Of course, it's possible that they won't have any of what you booked - especially HLEs which normally have smaller numbers of cars - in which case you're still going to be stuck with something larger.