I just bought a 2015 Corolla S Premium, and I do NOT have any "wandering" issues. I'm really quite happy with the ride and handling and smoothness and quietness on the freeway.
In contrast, "I absolutely know what you're talking about" with the wandering and such: About two weeks before I bought the Corolla, I had the opportunity to drive a loaner car from the same dealership for most of a day -- a 2015 Camry LE with about 1,200 miles on it. And that thing wandered ALL OVER THE PLACE on the freeway.
I traded a 2008 Camry SE V6 in on my Corolla, and I would say that the Corolla is actually a bit straighter down the freeway than my old Camry was -- the Camry ALWAYS pulled to the right at least a little bit, no matter what I did in terms of alignments and tires and such.
I would say, though, that the Corolla is a bit more susceptible to strong winds on the freeway than my old Camry was, but not by all that much.
In the end, I'm really very impressed with the on-road behavior of my new Corolla. I'm used to expecting utter garbage for OEM tires, but I just can't complain too much about the OEM Firestones. Sure, I expect to get "much better" tires when I replace them, and I'll go for "touring" tires that should ride smoother and be quieter, but I'm just not complaining about the OEM tires one bit.
At any rate, the Corolla S certainly has different tires and at least some different suspension tuning than the LE does -- perhaps it does make a difference in this case.