Most students will allow themselves to get hurt at least once before they follow this advice, which is why we generally limit the kinds of things new students are allowed to attempt (especially with younger students).
It doesn't matter if you think it's a "real" submission or not.
It doesn't even have to be a submission!
Cramp? Tap. Finger stuck in a gi? Tap. Partner too rough? Tap. Confused about what to do? Tap!
As you progress through the Journey, there will be times where you should push the limits of your threshold for pain/discomfort; times where you fight through a cramp; times where you deal with the fact that your partner is too rough; times where you resist that submission just a little longer... and during those times, you work through it, because hey: Martial Artists should not only avoid violence, they need to prepare for it, too.
The thing is, those times come AFTER you acquire the KNOWLEDGE and SKILLS to deal with them. It is NOT enough to simply have the WILL to deal with them.
To some extent, you probably have an idea of when to push things, and when not to. The trouble is, we often don't listen to our better judgement, because ego wants to win.
I get it. But the sooner you really accept that "losing" is often in your best interest, the sooner you'll get to the skill level that you came here hoping to achieve.
To tap or not to tap? That is the question! Whether it is nobler on the mat to tap against the armbars and heel hooks of outrageous pain? Or break arms against the sea of submissions and so end them? - Josh Oldfield