It's not about whether hospital staff washes hands, it's about WHERE.
We go into a bathroom after doing God knows what.
We use the toilet.
The hand we used to wipe turns on the faucet with a handle.
We wash it.
That hand turns off the water with the dirty faucet handle.
We use paper towel.
We open the bathroom door with the handle used by everyone who didn't wash after wiping themselves.
If we are a hospital staff member, we go back to the patient knowing we have washed our hands!
I'm going to bet that if we are going to eat we might take a paper towel to protect us from the door handle. Then there is no wastebasket near the door, so we give up and open the door with probably our right hand,
and go back to the patient. In the hospitals I was in last year, that hand may be the one that puts the liner back in the \patient's water pitcher by inserting all the fingers in the liner to push it in.
IN short, unless every basin is equipped with only a foot pedal, what do you think really happens?