I can't speak for all the people entertaining alternate theories, but it's not that I don't think she's a Skywalker. She almost certainly is. It's more than I don't understand why they would cloak it in secrecy when it's such a painfully easy conclusion to jump to that any small child could do it. Why even bother? Virtually no one would be surprised by that reveal and it seems like the point of hiding such a thing from the audience would be to give us a shock when it's discovered.
It could still be a surprise for the character, but if that is their intent, I would've preferred it if the audience was somehow informed in this film. Hiding it when the answer is the obvious one can only do one thing in this environment: induce endless speculation that will end up leading to a portion of the audience being unsatisfied when it's just the obvious thing anyway.
I think there's another reason beyond "shock value" that we would not be told Rey is Luke's daughter in this movie. The structure of the film is set up so that the plot of the movie (finding Luke Skywalker), isn't resolved until the end of the movie. Until the pressing conflict between the Resistance and First Order is concluded (destruction of Starkiller base). If Luke appears earlier in the film, sure, we can finally lean who Rey's parents are, but it would also undermine her character's arc of embracing her destiny, because Luke could just step in and wreck Kylo, saving the day. That's just sloppy character development for our new heroine.
Rey needs to hear from Luke first hand that she is his daughter, because discovering that truth will lead to a ton of questions that only Luke could and should have the answers to. But because he isn't found until the end of the movie, we'll have to wait for those answers.
I can imagine the truth being revealed in another vision sequence, where we see a youngish Luke instructing and training Rey when she was a little girl (probably usin some de-aging visual effects like they did with Michael Douglas in Ant-Man, hence the photos of Hamil a few months back with a fairly shaved face in Ireland; or was it Scottland? I can't remember), and we see her birth, some glimpses of her training, the academy attack, her memories being blocked, and her being left on Jakku in the care of someone trustworthy.
I don't think Rey was abandoned at all. I don't think she was left all alone. She more than likely had a guardian, and that guardian probably died/was killed when Rey was a teen, and she's been forced to survive on her own, with know known way to contact and inform Luke or anyone of her need for help. She hears stories of the Jedi and Han from various people that come passing theory the settlement. She remembers being left behind in the care of a stranger. She was under the impression that they'd come back for her. Those memories weren't blocked.
I think her comments about her identity being secret and classified were just her being dryly humorous about her predicament. She has no idea who she is, but then the force starts to move in her life, awakening within her, and latent ability in the force starts to emerge throughout the movie.
It's been shown throughout the entire 6 films that Skywalkers are gifted pilots and tech heads. From Anakin to Luke, they know some shit about tinkering and flying. Rey isn't Luke or Anakin 2.0, but she is definitely a Skywalker if her natural talent in the force, and skills with piloting are any indication. Her combat abilities were a result of her having to survive a harsh environment on her own. I think she's a very well constructed character. Her skills are more than acceptable, even her Force abilities when they finally start to overtly manifest.
Snoke says there's been an awakening in the force. The force is actively moving things into motion. Rey, as a Skywalker, has a natural affinity for accessing the Force. This, combined with her natural talents of piloting and scavenging and combat, makes her a very different character than Luke Skywalker, and even Anakin. Running from her destiny also sets her apart from her father and grandfather. Luke wanted to be a Jedi like her dad. Rey just wants to be reunited with her family. Circumstances out of her control (I'm fine with saying The Force manipulated thise circumstances) have her thrust into a path of discovery and acceptance of her destiny.
She's as much of a reluctant hero as Finn is, she just happens to be that reluctant hero that has such a natural aptitude for heroics. It's like the one guy/gal who we know that's so amazingly good at something, but has no inclination to pursue that line of advancement (I knew this guy who was an amazing artist. He even got a scholarship to an art college. He ended up dropping out and becoming an accountant because he didn't want to pursue a career in art, despite him being an insane artist. As an artist myself, I admit that I was envious and jealous, because I DID want to pursue a career in art, and would have killed at the chance to get a scholarship for art, but alas, I wasn't as good as him, but i digress...).
Rey's arc, if she is indeed a Skywalker, which I think she is, is going to be very interesting to follow. Kylo is also a Skywalker, so it could be great to see their dual journeys along their paths. He's going to become more dangerous than Vader, while she is going to become a powerful light side user like Luke.
We've yet to see a truly powerful light side user in these movies. We've seen some pretty powerful dark side users, however.