Good coincidence is OK-ish with consequences or foreshadowing. In the original post, if the woman taught the guy how to fight, but deliberately did a lousy job to set him up for failure, that might be interesting. He learns 90% of fighting and then the remaining 10% after he has an "AUGH! That b****!" moment. As for foreshadowing, check out nearly every James Bond movie. If Q gives Bond a cigarette lighter that explodes when its underwater and clicked twice, you know darn well Bond is going to be underwater when he needs explosives.
Bad coincidence is ALWAYS OK! In the 2001 sci-fi/martial arts movie "The One" starring Jet Li, our hero is running from the police! In a police station! And he opens the door and finds ... the police classroom where 20 guys are practicing with truncheons. Jet Li signals the comedic moment by slumping and sighing "oh no". Then the martial arts mayhem, which did NOT add to the plot, takes place. But its cool, because we believe random bad things will happen, so we buy into Jet Li randomly having to fight 20 guys.
Try to buy a random coincidence with a negative one. Maybe the best poke monster the guy coincidentally found is manic-depressive or something, I dunno.
For every question "Does thing happen? / Can hero beat the thing? / Is this good?" the answers are:
1. Yes. (almost always bad, unless it's the last chapter of your fantasy heartbreaking epic)
2. Yes, but ... (better! The best Pokebeast is available for free BUT it is manic-depressive.)
3. No (always awesome. The best Pokebeast is NOT available, the hero better sort this out on some kind of side quest)
4. No, and ... (best! The best Pokebeast is NOT available for free AND it forms a murder-suicide compact with the other Pokebeast the guy found)
If you need to write a coincidence to get your hero/heroine out of a tough spot, you've put them in a bad spot and need to rethink it.