Yes. That is exactly correct. If you are paying full price, they ask you what model, you tell them, you pay, you walk out with a sealed box. They do not activate in store (unless you ask them to). So there's no account created.
The SIM that comes in the phone is whatever carrier you said, but just pop in the SIM from wherever else you want, and you're good to go.
I just did it - walked in yesterday, bought Sprint model (A1865, which is the same as the Verizon model), came home and even before powering up the first time, I popped in my AT&T SIM. Powered up it up and was good to go.
ALL apple-sold iPhones are unlocked. Specifying the carrier only means it comes with one of those sims installed. If you try to order online, however, they will verify you are customer of that carrier (with the exception of T-Mobile - you can order that one online without carrier check, if paying in full). Even if you did buy a phone *from Apple* for Verizon and activated in-store or online, you could cancel at any time since from Verizon's perspective, you are bringing your own device. I've been told, if you never power the phone on with the Verizon sim in it, you won't even be charged the activation fee, but I don't have first-hand experience with that.
It's only if you buy through a carrier are they locked to that carrier. Presumably because you are likely financing through them as well. If you buy outright from the carrier, they will unlock it for you have some period (It's like 30-60 days). Verizon, by FCC rule, has to sell their LTE phones unlocked because it was part of some spectrum deal they made.