I am certain. I was a theory & comp major too. My girlfriend at the time was in medical school and I studied every bit as hard as she did, at least 6 hours a day not including practicing my instrument.

> My impression is that when you hear something aloud it's nearly always different to some degree from what you imagined in your head

For me and probably you, sure. For Beethoven, I seriously doubt they differed much at all.

The piano sonatas are ridiculously challenging and I'm more than willing to go along with you, but we could be wrong. I like your analysis and never thought about it that way. In general though as a (below-average) composer yes, I'm very certain about hearing things in your head. If I can do it he could do it with infinitely greater depth and efficiency.

About that particular piece, there's also the remote possibility of an editing or transcription disaster. He was not exactly thrilled with his publishers. More likely the former but I think you're right, the intent was probably there in his head.