Would you believe that Fang (Agent K-13) was played by the same dog that
played Jasper on Bachelor Father? His real name was Red, and he was
trained by Lassie's trainer, Rudd Weatherwax. But Red didn't take instructions
well, and that's why he was only used in a few episodes.

since I never saw "BACHELOR FATHER" I'll have to take your word for it.

I watched Bachelor Father during its original run, and the dog is very
similar. The information comes from Joey Green's book, The Get Smart
Handbook, so it is probably accurate. It is no more surprising than the
fact that movie star Benji was Higgins, the dog on Petticoat Junction.

I have no idea if "Red" was on both shows, but, from what I've read, Fang was written out of the show because the producers didnt like the character, who'd only been added by a request from NBC to have an animal on the show!
(They had also requested that Max live with his Mother, but, fortunately, that never made it to the show)