This is partially true both IMHO/IME.
For example, you take a ATT phone (obviously with non-emergent situations), use Verizon, *IF* you happen to be near what Verizon sems moving toards. A "bigger LTE netowor (and hopefully on cell standard,mostly and definitely finally!)
If you're near a CDMA (conly) tower you won't get any voice/text/data with a small set of
exceptions.
That pretty much sums it up for using the AT&T(mostly) phone on a Verizon line, you'll almost always get spotty connection, at best.
The overall point to make regarding using a phone cross-carrier, is not as simple as on would think.
You have to use something like FrequncyCheck, or look up the phone band(s)
If it only matches a couple of implemented frequency/bands (LTE AND CDMA)in your case) for that phone, then you'll either get "occasional" connection, but mostly none, in particular outside of metro areas.
The other thing that're likely to comes is the "updates issue", most carriers will ONLY provide them on a device with their active phone. If you do this, keep in mind that "patching things yourself) is pretty involved
There's also typically some domestic roaming that occurs, and no-one talks about, partly because (the majority) bigger cell companies have some sort of reciprocity (at least partial, perhaps full)
Roaming is sometimes locked to your cell companies, and will only work if you are using their service. This aspect does seem to be changing though, for the good.
The one other thing that're likely to comes isup are updates, most carriers will ONLY provide them on a device with their active phone. If you do this, keep in mind that "patching things yourself) is pretty involved