It sorta counts. I mean, Hardware Wars, Spaceballs, these were legitimate reflections of the OTs influence and status in culture.

The difference is that the PT doesn't have anything that mocks it out of respect that isn't Lucasfilm sanctioned or co-produced (i.e. Robot Chicken, Lego Prequels). The PT does have an influence, but it is only in the critical sense. You have Simpsons episodes where people argue about which prequel sucks more, etc. The PT has become a model example of "the bad film." Most actual bad films aren't remembered a year or two after they come out but the prequels seem to have endured in peoples minds in this respect. Noone really knows who Watto is, and he was one of the best characters from the PT, but everyone could spot Jar Jar from a mile away because he was so legendary for being annoying. If you ever see any lasting positive impact from the PT it is usually due to the OT references--Vader, Obi Wan, R2D2, stormtroopers, etc. The PT has kept the memory of the OT alive and well, but its own identity has not stood up well except in the parody department.