Yes, tremolo requires lots of work for most people. However, tremolo is also a product of a well developed right hand technique. I have had many students walk in my studio wanting help with tremolo. In my decades of teaching, there was never a single incident where the student seeking tremolo help had a good right hand foundation. Usually, it was many things that needed refinement in various right hand movements.
There are so many things that have to be developed with various right hand patterns. There are particular sympathetic movements where fingers learn to work together. There are particular opposing movements where one finger must flex while another extends and vice versa. This is necessary preparation for learning the difference between walking and running. It is a delicate procedure to approach in lessons because each student is unique. As an extreme example, some students benefit from a very detailed and contrived practice of these slow movements. For other students, the cure is worse than the disease: having a general understanding is necessary, but too much attention to details has the opposite effect. Regardless of HOW the topic is carefully approached, it is a foundation of "effortless" right hand playing.
Further, sometimes there is string crossing required demanding a mastery of subtle shifts from the elbow or shoulder similar to scale practice. Christopher Berg's Giuliani Revisited is a required book for all of my students, and is something I use myself every single day. Berg's revisions demand students and teachers together to investigate similar right hand patterns where fingers may or may not share the same string.
Then there are bursts or (sprints). Sometimes, these bursts help a student find some of the things I wrote above more naturally. Sometimes they come after some more fundamental careful study. Rhythmic variations play a similar role.
Tremolo requires and mastery of everything I have written above. And to repeat, it is merely a product OF that mastery. While tremolo certainly requires consistent work, it FIRST requires a very strong and well rounded right hand. With the guidance of a competent teacher, I believe Berg's work is a staple that must be on every students music stand. In addition, Stanley Yates' Classical Guitar Technique is a work that tries to put some of these ideas in writing, and also details some specific exercises helping students to better understand these foundations.
I don't know which teacher said the right or wrong thing; I wasn't there and I have no context. Quoted out of context, it is possible that I could have said either statement.
So, which teacher is correct? The one who emphasizes some of the ideas I wrote above and is constantly refining more basic movements.
Dr. Todd Tipton, Noda Guitar Studio
Charlotte, NC, USA (available via Skype)