Yes, 100% truth. Verizon's LTE uses a "technology" called eHRPD - it helps the handoff between 3G and 4G move faster. But it's more of a clunky way to make both 3G and LTE work, honestly.
The problem is, if the LTE network is struggling (or down), eHRPD is somehow affected by this as well, causing 3G (only on 4G phones) to also struggle or go down. Honestly, that's one of the main reasons I've switched back to a 3G only phone for now, until they get it working better. If it switched to Verizon's normal EVDO Rev. A 3G network (which is still technically there, eHRPD is just "on top" of it) and stayed a consistent, reliable connection, that would be one thing. But, in my opinion, it takes away the #1 reason that I personally pay for Verizon - reliability.