Well you could appeal and tell them your circumstances but…
From the back of your {paper counterpart} licence:
“You must tell the DVLA at once of any change of your permanent address…………..etc.,
Failure to notify any changes as described above is a criminal offence, punishable by a fine up to £1000”
Think I’d just pay it, you did get the bike free after all (and maybe a load more if your sister now has the house 😉)
AFAIK without possession of a V5 in my name I couldn’t tax it
Yes you can:
“You can tax your vehicle without a V11 reminder letter using a: V5C registration certificate (logbook) in your name if you’re the current keeper. V62 application for a registration certificate if you’re the current keeper. green ‘new keeper’ slip if you’ve just bought the car (and do not have a V5C in your name yet)”
Was it even insured?