I don't know how strict you are in your understanding of "playing as Beethoven intended, as per the score", so this might make it tricky. When we work on music, we do make use of the Net (not necessarily YouTube per se) in a particular way. We work on understanding the music from the score first. This assumes some knowledge of theory, genre etc. The way I've been taught by more than one teacher, scores are not to be understood literally, i.e. not literally 120 bpm, not total strict following of dynamics or anything in a robotic mechanical way. That is not "as the composer intended". But you also can't just go off and do your own thing. That's where a teacher guides in what the parameters are, and what kinds of things you can do which are right. Often my teacher demonstrates various ideas.
We then also go to Youtube (Internet). We will study what various performers did, and figure out why they made those choices. It is not for imitation, but for understanding. Sometimes there will be other factors. For example, old pianos did not have the same degree of sustain, so the music might be played faster, or tastes were different in the past. Youtube together with a teacher, can be very enriching.
The other factor is what a student is actually capable of doing at a certain point. Students are themselves works-in-progress - not just the piece. If you are just mastering how to keep steady timing and handling relative note values, it may not be the time to experiment in rubato. If your technique is up to a certain point, then it may not be time to be doing other subtle things beyond your capability. In my own studies, some of the things I see are shelved as "for a future time - for now do it simpler". As a student, it is good to know that certain abilities need to be acquired, and that creates a motivation for working on those technical skills.
I'm writing as an adult student, but I believe that young students are also given a chance to see how something might be played in the future when they have more skills. Of course, pieces are also selected according to a student's level.