Signs are there because there are a lot of everyday germs out there that we pick up on our hands from our everyday environments. Most of these are the germs people are talking about when they say having a little dirt on them helps children build immunity when we're exposed to them at a low level.
Here are just some of them:
Influenza
Norovirus
Klebsiella
Shigella
CDiff
Haemophilus
Hepatitis A
Staphylococcus
Pseudomonas
Streptococcus
We get them from:
Money
Doorknobs
Cell phones
Faucets
Used tissues
Pens
Computer keyboards and mouses
Shopping carts
Steering wheels
ATM machines
Bathrooms, etc.
There are hundreds of strains of EColi. Most are normal flora of the human gastrointestinal tract, and not only aren't harmful, they can actually be helpful. (And yes, these types of EColi can be on hands, too.)
However, there are some types of EColi that produce a shiga toxin that can produce violent illness, and even be deadly to humans, but live harmlessly in the guts of ruminant animals. One would not normally find these types of shiga-toxin producing EColi on hands.
BTW, I was not the first person to bring up the latter type of EColi on this thread. Another poster shared she had a friend whose child almost died of EColi.
I was just discussing the differences in the bacteria, and then pointed out, after the OP mentioned her experience at the dairy farm, that I found it funny that she was worried about the chips, but not the dairy farm, when one was well known to be so much more potentially harmful than the other.