Just curious... If any country sent me a bill for my US registered
aircraft and I'd not flown it in that country, I'd tell them politely
that it wasn't me and then ignore all further communications from them.

I agree and tried that. I got followup invoices with late fees and penalties.
The US has some sort of obligation agreement to help them collect fees, so the US gets involved too.
They eventually assigned a debt collector to harass me.
I finally had to get an attorney involved.
I spent far more money fighting it, than if I had just paid the tolls, but then it was the "principle of the thing" and I am stubborn.

When you see how much of the money goes to the "administration" cost of these systems, it is really sad.