Except for KeyString, you folks are steering clear of the second, potentially more interesting part, of Bluoh's oroginal question:
(b) Is it possible for a beginner to interpret a piece of music entirely on his or her own? (I.e. No demonstrations of the piece, no videos, etc.?) Why or why not?
Any particular reason?
There is a problem with that question, Ed, and also the answer you've give so far, if it is to be seen as "the" answer. The problem is that teaching is a process where something is developed over a long period of several years, and teachers may come from opposite sides to meet at the same destination. Any individual teacher may also make different choices for different students. We'll leave out poor teachers, in this.
Take these two opposites: the ability to play timing and note values and meter with relative accuracy - the freedom of feeling the music, being creative with time for expressive purposes. You must be able to maintain the pulse even with rubato, and you have both elements occurring in music. Some teachers may start with freedom, and bring in the accuracy later. Some may start with accuracy, and bring in the freedom later. Many may toggle both ends of it. Any attempt to say that one particular approach is the right one is misguided.
The same goes for anything else. I am a creative, self-directed person, and have been so from earliest childhood. But there are times when imitation has served me well. Sometimes imitation can be a step in getting something into your body which then goes toward your senses, and ultimately understanding. Sometimes the understanding will lead musical choices, which then translate directly into playing. Either angle may be appropriate in various circumstances.
I think that what you are objecting to, Ed, is this idea of listening to a CD in order to find out "how it goes", and then copying that CD. In general I don't feel comfortable with that idea either.
Other elements include gaining an understanding of music. What is the general mindset of the Baroque period or the Romantic period? If a piece is based on "dance music" and they actually danced to it during that period, what type of rhythm do the dancers need, and how did they move at that time? Will the student learn this theoretically, maybe watch such dancers (easy with the Internet), and then try to bring that pulse into his playing? Or does his teacher first model the rhythm, to be copied by rote, and bring in the understanding afterward after a few pieces have been played?
One elephant in the room involves competitions or exams, and "what judges like to see". This may restrict the creativity and imagination of both the teacher and the student. Here you may get into imitation, looking at performances, not for ideas, but as models of "what is acceptable".
I don't think that this is a simple thing, with simple answers.