This is either bad writing or it's intentional. Some will argue it was their spot originally because the stuff with Zack was retroactively put in after the OG (even though yes Cloud and Aerith basically spent almost no time there.) Or lets look at the scene for what it is, the recreation of a memory she had with Zack in CC, aka the "Zack date" where I would argue Aerith begins to act a little more like her CC self, she even replicates the line of treasuring the item given to her just as she does with the pink bow in CC. The scene is littered in Stamp/Zack imagery that if you look around as Zack in as Chapter 8 the Stamp stuff isn't there (Like the Stamp dog you can choose for Aerith on the Hairclip stall.) Hell there is even a poster in full view of the Photo you are posing for that portrays the Stamp/Zack dog carrying an injured yellow/blonde dogwith the bandage around it's left arm. Hell we even get multiple Zack cutscenes during this date.
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What happens during the entire date? Nothing goes right, why? Because you cannot relive a memory hoping for the same spark when the person who you made the memory with has been replaced with somebody else. This is why I think in the HA version of the Church dialogue (in the Japanese version I believe) she gets momentarily excited when Cloud suggests they should make new memories, because she knows this is an old one and she has no other happy "date" to pull from.. but then also realises she isn't necessarily feeling the same spark she did with Zack. Sure she likes Cloud -- in here own words -- but also in her own words she doesn't seem to know how much she even likes him and now she "Knows where (they) stand", and the sad part about it is she knows she will unlikely ever get the chance to explore more, hence NPTK which in the Japanese lyrics sound more like "I want to be able to spend more time with you in order to figure out what i'm feeling, but know i'll likely never get the chance" rather than "I love you so much please take my hand and we can be together forever" which I think makes no sense for when it is performed and written.
Oh and uh as for the Church, what happens after Aerith basically has to spell it out for Cloud what "our spot" is and makes him follow her? We cut to a scene of Zack sat right outside the Church. I have to think this is intentional, why? Because if she had said to Zack lets go to "our spot" Zack would have immediately known what she was talking about, I think part of the reason Aerith talks about knowing where they stand is because unlike Zack, Cloud didn't immediately know what she was talking about, and like most "romantic" interactions between Cloud and Aerith, Cloud basically has to be "cojoled", as she says on the date, every time to get even half the responsiveness that Tifa gets and that for her is reason enough to realise that Cloud just isn't responding to her in the way she necessarily wants him to.
It's about Cloud and Zack, the only person that has commented on saying it's strictly about Cloud is Loren Allred in a recent interview who said she looked at wiki and youtube and such to gather information. I will be interested to see if the Zack info comes out over the coming months, i'd say watch this space.