I'm not sure anybody can hold back information, or more likely - if they claim they're holding back information they're probably lying, or they're just not that skilled. After doing martial arts for a couple of decades - you realize that there's not much variation between the different styles. Really there's only proclivities between the various historical masters. Sometimes that leads to stagnation because modern masters and students can become afraid to experiment... or experimentation is looked down upon. The only holding back that seems to happen is that some masters are rigid and don't allow flexibility with their students. This can take different forms but usually it's a variation of this thought of my style is the best and has all the answers so don't look outside it and definitely don't cross train or I'll throw you out and I have all the answers.
I have this theory that there really are only a few martial movements and these are pretty much universal. The movements can be interpreted in nearly infinite ways hence all of this thought of hidden applications or secrets. When one really explores - they become aware of these secrets which aren't really secrets - they're just discovered personal proclivities. This happens naturally over time.
To illustrate a more concrete example of this theory: One of my new favorite forms is one that I learned in the third grade from a traditional Okinawan stylist. It's Naihanchi Shodan. It's a controversially boring form which most people initially hate and then grow to love. Its genius is that it is a super nebulous and vague form. If you look up the form you'll find a plethora of masters talking about hidden techniques and meaning found in the form... and everyone seems to have their own take on what those techniques are. Here's the big secret: They're all correct. I think the vagueness of the form allows for something unique... which is - after a couple of decades of martial study, if you go back and do that form, you'll start to see all kinds of shiznit in that form because it's like a living rorschach. You find techniques that you want to find based on your own proclivities.
If I'm correct, how can any master keep anything secret? Especially if a student is earnest and puts in the time because they should discover their own secrets.