Also have to keep in mind, that the OEM Corolla brakes are not something that are designed for continuous high speed braking. Eventually, you will overheat the friction material and potentially strip that smooth brake transfer layer off the rotor surface. This will lead to uneven braking (vibration at highspeed). This also assumes that your tire balance has not changed, tire tread is evenly worn, hub and wheel bearing are OK, suspension is sound, and steering is fine.
I've got that vibration issue on my Matrix last few months - recently changed the pads (showed about 1/2 wear but were overheated from some heavy emergency braking) and replaced the rotors as a precaution old ones were starting to corrode badly from the salt in winter + they are pretty cheap to replace (Brembo blanks ~ $53 @ Tirerack). After bedding in the new brakes - no vibration from highway speed braking.
I also have to note that the OEM system has only adequate heat capacity (rotors are averaged size for size and weight of car) - any extra loading from heavy brake usage (ie, multiple highway speed stops, or panic braking from high speed) - will put a tremendous strain on the brakes. Sometimes you will experience "shuddering" with the first application of brakes at high speed. That is normal - not much you can do about that - as that is a limitation of the hardware on the car. But if this continues or gets worse at those speeds, then there is a good chance that the pads are cooked/glazed, rotors are glazed or overheated (bluish tint), or brake transfer layer is wiped away.
Here is a good article on this brake transfer layer - http://www.stoptech.com/tech_info/wp_bedintheory.shtml From one of the top manufacturers of braking systems.