Its more a sign of both - the student's willingness to adjust and the teacher's willingness to refine. The reason I say both is that you run into students that have a better chance of picking something up right away (prior experience) and others that do not. The student that does not have that prior experience still needs it in order to be successful. A good instructor knows not to only focus on the people with prior experience and help boost the latter as well.
For example, in martial arts (as I noted elsewhere), you have someone who has prior experience in body coordination, which makes it easier for them to pick up an art (or dance or a sport). A student whose never stepped on to a mat in their life still needs body coordination. While a good instructor should see that and help build that coordination, the student needs to develop motivation and discipline to do these things without the need of someone else. An out of shape student should needs to recognize they need to put in extra work to move up a level - that is something the instructor can only point out.
A great book I use as a backing to my teaching philosophy is Mastery by George Leonard[1]. It categories the different personalities of the student into Dabbler, Obsessive, and Hacker (not in a good way). Dabblers try but quit when things get hard; Obsessives consume everything possible until they start seeing diminished returns; and Hackers just kind of "show up" and steadily maintain/improve. People can be all three for different things but its handling the particular category appropriately that pushes people toward mastery.
[1] https://www.amazon.com/Mastery-Keys-Success-Long-Term-Fulfil...