Both words can be used here. Collins Cobuild picks up on this reasonably common usage of where:
... 5. [conjunction]
You use where to introduce a clause that contrasts with the other
parts of the sentence.
- Where some would have given up, she and her coach were determined to lift their game.
- Sometimes a teacher will be listened to, where a parent might not.
[COBUILD Advanced English Dictionary]
AHD is clear here:
where [conjunction] ... 3. Whereas:
- That model has an attractive design, where this one is more dependable.
I'll admit that I'd use 'while' in AHD's example, as it both compares (two pluses) and contrasts (pluses / drawbacks).
Fleshed out, 'in situations / a situation where' or in OP's example 'The situation once being that', followed by a contrasting second statement ... but then these would sound clunky. In fact, OP's second variant sounds stylistically better to my ears.