This makes perfect sense to me- I have thought about this before, and I think this is very probable.
I experience this sort of thing sometimes when doing a series of readings on a particular subject. For example, a few months ago I did some readings on a particular person. The high priestess card kept popping up, and I couldn’t’ quite understand why- the obvious traditional meanings didn’t quite seem to fit. Then I realised that the person has their moon in Pisces. Ah OK, I thought, Pisces = High Priestess. So every time I do a reading on this person and this card appears, I assume that it is somehow related to their moon in Pisces, that that particular aspect of their personality is someone influencing the events. Of course I can’t be 100% certain either, but that’s what my intuition was telling me.
Another example is the 6 of wands. When I first started doing tarot, the first book I bought said that if the 6 of wands appears as an answer to a yes/no question- it will always mean yes. So for me, this card now means ‘yes’, and will often appear as the answer to a yes/no question even though I’ve shuffled the entire deck and the chances of this card appearing is obviously quite slim, yet it does, because that is the card that means ‘yes’ for me.
I realise this is not exactly the same as the situation that you have described, as the cards in my example are still related to the traditional meanings, but I think it still shows how the cards ‘personalise’ themselves. I really do think that with tarot you need to let your intuition guide you, just go with whatever ‘feels’ right.