It is absolutely possible - they need to only have loaded pricing incorrectly, or left old tickets out, or experience a technical issue. It happens to my past and current (retail) employers so why would Foodstuffs be any different. Again - anecdotally, I have receipts from NW where it clearly says my Clubcard number but the pricing has not been applied, and yes they were surprised by this.
Also I understand how Clubcard works and I appreciate it's by design that scanning Flybuys or Airpoints card doesn't get you the discount. I was mentioning it for people who aren't aware and also pointing out I think it's a stupid system.
It would be incredibly rare for a price to be loaded incorrectly, if it's a store without ESL then you could have an old ticket still up, but that's going to pretty quickly show where the problem lies. In a store with ESL it's pretty much impossible to have pricing not match (well there are a couple of scenarios, but they involve major human or technical issues and would result in thousands of prices being wrong).
People only scanning Flybuys or Airpoints cards is pretty much non existent - literally 99.9% of people who scan a loyalty card use a Clubcard.