Yes, that'd be the one I think. It's slightly borderline - I don't have enough legal experience to know if, in a case where the extension was purchased before departure from the intermediate station but where it was blatently done because the passenger saw an inspector, such a charge would stick or not. Though in principle going from Euston to Bletchley and extending at the last minute to MKC is something someone might do, e.g. because they forgot where they parked or found a larger availability of hire e-scooters at the other one*, but going from MKC to Bletchley and extending to Euston is not really a genuine use-case you're going to get very often if ever.
* I've very occasionally done it for the latter reason. Fairly large swathes of south-west Milton Keynes are effectively between the two and both are useful.
The passenger didn't board a train at Bletchley, and had a valid ticket upon boarding at Milton Keynes C, so cannot have committed a byelaw 18.1 offence.
If a ticket was presented to the inspector then no byelaw 18.2 offence occurred.
If a BLY-EUS ticket was purchased before the train left BLY, then no Regulation of Railways section 5 (3) offence occurred.
So if we take all the OP says as being true, it does not appear to me that an offence was committed on this occasion, even though the OP probably intended, when boarding at MKC, to commit an offence. In a situation where no offence was committed, offering to pay a settlement to not be prosecuted is odd.
This is based on the information the OP has provided thus far. The story keeps changing, and if it changes again, my answer may well change again too.