Perky looks like a good quality purebred jack to me too. You may not be used to seeing them in b+w but what if you turned the black into brown. Everybody would know what she is then.
oh I agree, she does indeed LOOK like a pure bred JRT, we question it based on her behaviour, she does not have one single behavourial trait that fits that of a terrier, her behaviour is the complete opposite of a terriers.

Terriers:
love to sniff out vermin
no problem getting dirty
extreme energy, no off switch
like to fight
feisty
indepentent

Perky:
is trustworthy with my gerbils and afriad of my rabbit
will not set foot in anything wet or dirty
energentic considering her age, but not even a fraction of a terriers energy, she is more then happy to sleep the day away
no interest in fighting, only fights if the other dog started it
not the least bit feisty
extremly clingy, she has not a shred of indepence