A very interesting question. I think we should address first the differences in musical practice.

If we listen to recordings of the last decades and compare them with early recordings, we easily notice differences. Performance practice has switched to note-perfect performances, with more precise pitch ( we see that even in piano tuning... The Piano Technicians Guild has made standardized tests, and aims to raise the precision of the average technician).

Can we say performances are of a higher standard because we play less wrong notes, with more precise intonation (for some specific definition of intonation)? Or because our rubato is less "extreme?" It is not always productive to judge the past with our current standards. Our idea of what a good interpretation is seems to be different from what it was in the past.

Musicians before the 20th centuries had different goals. They were not playing the canon non stop... They were actually presenting new music very often. We can now listen to a thousand performances of the same symphony, one after the other. In the past, people asked for complete works or specific movements to be performed again (not having the certainty of being able to listen to it again for a while).

Note-perfect renditions of "a work?" Yeah, people sight-reading a new work and improvising ornaments didn't have the same concerns we now have if you work for 1 month on one work (that you might have been listening to since you were 8 years old, and you might have already played ALL of the other similar works by the composer during the last 5 years). Super fast tempi? If we are into that then sure, but people in the past had different ideas of what an "expressive" interpretation was...

So yeah, I think we can say our standards of accuracy, pitch, rhythm are more demanding; we can say our performances are of higher standard if we use OUR standards. Why should we exclusively use those standards? Can we be sure our standards are a good thing to have?

Your professor sounds like somebody who is into the mainstream classical music culture developed since around the 1920s. Nothing wrong with that, most of us classical music people study and work in that environment. But there are other ways to see this.

How do we know about the standards of yore? Well, we have treatises, scores, letters, newspapers, diaries... A lot of people talked and wrote about their views on music, and historians/musicologists have worked hard to make sense out of that. Couldn't we be wrong? Yes, we should assume our conclusions are not final. New eyes take a look at the previously studied evidence, new techniques are applied, new experiments are conducted ("historically informed performers" have tried to revive the musical practices of the past, not just about them)... We have learned A LOT about old music in the last 200 years. We will probably learn way more in the future.

You might be interested in reading Bruce Hayne's The End of Early Music: A Period Performer's History of Music for the Twenty-First Century. A very nice book that deals with the differences in performance practice. Read Hayne's book, it is HIGHLY opinionated, but it is a very nice book.

It is due to the birth of recordings. Once recordings were available, people became more focused on being perfect (pitch, rhythm, etc). Glenn Gould is a pianist who basically devoted his whole musical career to just creating the perfect recordings. He would sit at the recording studio re-recording a single piece multiple times until he thought it was perfect.

Now when your professor says "higher standard," it is just his opinion. If you listen to cellist Jacqueline du Pre and Yo-yo ma you can see the difference. Yo yo ma has perfect technique and is a lot more mechanical to du Pre's playing, relatively speaking. Jackie du pre was a lot more concerned in her expressivity, not to say yo yo ma wasn't. So if your teacher thinks higher standard, I would probably disagree. Music is music and it is always open to interpretation. Yes, we've learned a lot and developed tremendously in how we interpret music, but to say it is to a higher standard is just his opinion on his scale of how good or bad.