jumping/jetpacks seem to break the grip. If you spin fast enough you do get a fraction of a second to shoot the basilisk if its behind.
That's what I'm talking about

. Although I must admit, I haven't tried it with a jetpack (if I buy a jetpack, I fly around like crazy, and only land when no enemies are nearby

). So Basilisks have a hard time to get me (ok, if some noob deconstructs the Reactor while I am at the Alien base, it would probably happen

).
Jumping ain't helping much, but yes, when rotating the mouse very fast, you can shoot the little bastard (but true, just for a fraction of a second). That's why I think high sensitivity should help. (This wouldn't affect me, if I played Trem 2 years ago - I was using a sensitivity of 15

).