This isn't correct. I've had a New Jersey E-ZPass in the past and have the Massachusetts version (called Fast Lane, but it's the same) now. I never set foot in any physical location for either. All transactions were done online, with the transponders showing up a few days later.

There may be states where you have to show up somewhere in person, each state runs its own operation and makes its own rules, but that's not universal.

I think I had to identify the car the transponder would be used on. That might be difficult for a rental you haven't picked up yet, but there's no rule limiting it to that car. I've used mine with service loaner cars more than once. Just be sure you put down a valid registration and that, if it's not yours, that you have the owner's permission to do it.

Personally, I'd get one. The delays in cash lanes can be long enough to be quite annoying. Using non-toll roads isn't an option for much of your trip if you don't have a lot of extra time.