Picking mice up.

I took my mouse (1yr female) to the vet for a checkup.  She's perfectly
healthy, but I needed a certificate to that effect to present to US
customs when I move next week.

The vet (a 'pocket pet' specialist) tried to pick her up by pinching
the skin at the back of the neck.  My mouse emitted a high-pitch
screech and promptly bit the vet.  She had never uttered a single
squeak before and never bitten anyone (even while being tamed).  Then
again, she had never been handled like that before.

Is that the standard way vets pick up mice?  Does it usually work?
Normally I just extend my hand and she hops on.

The vet gave her a clean bill of health, issued a certificate
(containing five errors), and charged me $75 for the privilege.