A more fair comparison would be a higher end Camry, Avalon, or L Series Lexus.
The Corolla is a very simple car in every respect and inexpensive. Reliability goes down when systems get more complicated and expensive. That's why the Acura and Lexus equivalents of there Honda and Toyota counterparts are much less reliable.
Lexus was the most reliable automaker according to consumer reports for awhile. Mazda I think recently dethroned them but they are I think still above regular Toyota. Not sure what your source on this claim about Lexus being less reliable than Toyota...
My source is Consumer Reports. CR lists Lexus as a brand of the Toyota Motor Company, and yes Toyota is the most reliable automaker. But if you look at Brands, Toyota, Honda, and Subaru beat Lexus.
Mazda was never in the running. Mitsubishi has better ratings than them.