The back of an ambulance is not a sterile environment, for the most part, despite how much (or not) we clean it.
But then again, we do lots of silly things. We take our suction catheter out of a sterile package, lubricate using sterile water, then stick the thing into the patient's very UN-sterile mouth.
We glove up, not only for our safety but theoretically for the patients... then we wear short sleeves, and a wristwatch, and wear the same clothes from patient to patient and, when it gets cold, the jacket we haven't washed since God knows when, provided it doesn't have blood all over it. I seem to recall there are studies saying Doctors' neckties and lab coats are vectors for disease, and I'm reasonably certain EMS uniforms are in the same boat - I'm sure that we're not helping hold down nosocomial infections, especially when we traipse right from that infectious patient to the one in nursing home filled with immunocompromised geriatrics.
I'm pretty sure it's required that every ambulance carry disposable gowns. Has anyone here EVER put one on? How about for a call that wasn't a childbirth? I think they're in the same cabinet in the rig that holds the N95 particulate masks and the surgical masks with face shields... By the way, I had a suspected meningitis patient, and when we walked into the ER, my crew and the patient were all masked. I caught /such/ hell from the nursing staff.
Taking vital signs without gloves on is probably the least of the things we're doing "wrong".