My take on Rey's force competence is more along the lines that when she resisted Kylo's mindprobe to the point of reversing it, she also inadvertently got a hint of what training he does/did. Combined with the stories on Jedi she read, and well...
Despite my general incredulity about the whole affair, that was what I gathered at the time from external view of the mental tussle over the memory of the star-map.
A great but untrained (force-)mental strength pushed around by the weaker aggressor. It'd be like you never having had to fight before but finding you had unusually strong bones, thick hide and extended stamina when you're set upon by an unarmed juvenile street-thug. He keeps hitting you, perhaps knocking you down, but he can't stop you from getting back up again, and you realise that he's just swinging at you in a frenzied but predictable manner that you block and dodge until he's worked up a sweat. You're probably capable of trying some hitting back, but he's not willing to act as
your punchbag, so that's when he gives up and runs off. That's what happened in the interrogation chair.
Rey has felt the flexing of mental muscles she never realised she had, nor exercised. It's an
excuse, therefore, for her to explore that mental musculature and put the Jedi glamour on the guard (not quite getting it right the first time).
But it still doesn't entirely work for me. She's only just learnt how to roll with the punches, and now she's trying to master the non-physical version of Drunken Monkey, or some-such advanced martial art, which leads the opponent into a merry dance entirely of the practitioner's choosing.
And by the time of the actual physical fight, she
totally requires Ren's distracting injuries and her own previous (perhaps unconsciously always Force-mediated) staff-wielding skills to even things up. But there's no room for mistake on her part, given that it won't be bruising she gets if she lets through a strike. And this is a one-bladed sword she's swinging, not a double-ended staff...
Ren's the one making all the mistakes. He's already almost not bested someone who not long since would have been considered cannon fodder. And on the edge (quite literally) of an advantage he lets her smoothly progress into a trance-state that, amongst other things, activates the stirring background music and rallies to a geologically-created stalemate?
The only explanation is that there's always a large amount of base instinct to Force Use in the best Jedi. The amphibian autonomic hind-brain, the mammalian behavioural mid-brain and the human (or galaxy-far-far-awayian equivalent to each of these) sentient fore-brain is further supplemented by the spark of Jedi Essence in some way, at some point in the system. It's how young Annikin "Yipee!!!" Skywalker so intrinsically understands mechanics and podracing, though he doesn't know it. (And I
refuse to talk about midichlorians, outside of the Darths And Droids treatment!) It's how Luke has always been a good natural shot. It's probably what made Han a good pilot in both his time in the Imperial forces and afterwards (although he was never more than a
latent Force User) and how he
always often enough managed to talk his way out of situations when black-market deals got a bit sticky.
If it's genetic (and still denying the existence of midichlorians!) then the son of Leia and Han could still end up lacking the gene, or leaving it unexpressed or poorly expressed as a single recessive copy, poor Ren who has the upbringing but not (yet!) either the inner strength or even the physical strength to weigh down upon a backwardly prone opponent. And I think then we're pretty much guaranteed that Rey
is the daughter of someone with a Jedi Gene, even if we can't say for sure that it's the one person the film seems to want to telegraph to us ('cos it
could be a bluff, without Lazy Lucas behind the script).