Sure, you can come up with scenarios that would fit.
But the OP needs to come up with one soon I would suggest, as thus far he is unlikely to convince.
Fares:
Off-Peak single £13.60
Off-peak day return £13.70
Off-peak return £22.70
I would imagine you'd remember if you bought that more expensive ticket, and why.
I agree that the OP has questions that they need to answer. But I cannot agree with your assertion that buying an off peak return, or rather, not having an off peak day return means that a reasonable person would find it suspicious.
If I am suspicious of the OP's story, it is not because of the type of ticket they held.