First of all, that's mostly untrue. But the thing with Mozart and Beethoven is that in their time, the way to have proper technique was probably widely known. Mozart probably learned them from someone, early on, and then applied them himself.
Yes, I do believe that the teachers of Liszt, Chopin, Bartok, and Hoffman taught them technique. BUt again, with Liszt and Chopin, all this stuff was used a lot more widely. Today, less and less teachers are teaching correctly.
Mostly untrue?
Mozart took piano lessons with his father, a violinist, and with his sister, a child. Then went on to revolutionize piano techinique to heights undreamed of at the time. Start by emphasizing that pianos were a relatively new instrument. There is nothing in the keyboard literature prior to, say, K283, that nearly approaches what Mozart was doing at the keyboard. Self taught.
Beethoven took piano lessons with, among others, Neefe. Compare any Neefe piano divertimento to Beethoven's Op2#1. It bears no comparison. The closest influence on Beethoven's pianism was Clementi, who was not his teacher. Self-taught.
Rachmaninov and Lehvinne studied with Zverev. Who made them play drills a la Hanon to no end. They do have around, though, Anton Rubinstein and a bunch of other Russians that can play the crap out the piano, and they watch them. Rachmaninov goes on to write, at the beginning, things like Op. 3#2, which is quite within the realms of the pianistic writing of Liapunov, Balakirev and Moussorgsky. But then he "teaches himself how to play the piano" and goes on to write the good stuff, Op. 31 and 32 and the concertos, which are - I would say - somewhat removed from what poor Zverev tortured him with. If you seriously think Zverev taught Rachmaninov what Rachmaninov knew about playing the piano, it is a waste of my time to show you otherwise.
The others are more obvious. Contradict if you can. Your last sentence is so deep in the senseless, from about any point of view, that I will leave it at this: today we have more incredible piano teachers (and pianists) than EVER before.