Professors certainly matter to students. I had one [award-winning] Art History professor who was very accessible despite teaching popular 1st year classes with hundreds of students. I also had a stats prof from China who could barely speak English...
Great professors still matter sure. The problem is that there are so many more resources for learning thanks to the internet. 50 years ago, a bad economics professor was still somewhat acceptable because the alternative was learning nothing about econ. But now, there are dozens of great economics books available for next to nothing on Amazon and dozens of really good econ blogs to follow. A decently motivated student can learn quite a bit from these resources.
A great professor will still raise above the competition and make an impact on their students but the poorer professors are a joke.
The Internet's changed the world of education. I can tell, in some of my classes, which of my fellow students were "raised" on the Internet and which weren't. There's a surprisingly large group of people that's stunning professors by understanding the subject matter on a very deep level.
There's also a professor who I doubt knows as much about her subjects as some of her students, or at least isn't teaching like she knows what she's talking about. I think it's very possible nowadays for students to know more about part of a subject than the person that's being paid to teach them.