Again, you are not correct. LTE is based on the GSM technology 'family tree', and was designed specifically in that way.
Who told you that?
Sorry but there is no 'family tree'.
LTE is a clean cut from UMTS which itself is a clean cut from GSM. OFDMA is fundamentally very different in principle from the TDMA principles that GSM is based upon. GSM itself grew from the 1st gen TDMA.
Who implemented the first UMTS network? Docomo. They implemented UMTS without even implementing a GSM base station network. In fact, in Japan, GSM doesn't exist, its all straight UMTS with Docomo and Softbank. If the station network is degraded to the point you don't get 3G, there is NO EDGE, NO GPRS the connection falls back into. Oh, and there is a good reason why UMTS is also referred to as W-CDMA --- it uses Code Division for multiple access and spread spectrum and like 2G CDMA.
Another country that implements UMTS without GSM base stations is Korea. They went straight from CDMA to UMTS using the same stations. As a matter of fact their phones do switch between CDMA and UMTS and with one telecom, EV-DO. Again, no fall back to EDGE or GPRS.
For that matter, when Verizon implements LTE on the Thunderbolt, there is no fall back to UMTS and no fall back further to EDGE/GPRS.
The family trees goes like this:
TDMA - GSM - GPRS - EDGE
CDMA - EVDO Rev A - EVDO Rev B
(EVDO isn't a clean break from CDMA and still use CDMA channels for voice and text. To have EV-DO, you still must have CDMA base stations. UMTS doesn't have that kind of relationship with GSM.)
UMTS - HSPA/HSDPA - HSPA+
LTE - LTE Advanced
WiMax
TD-SCDMA - TD-LTE (combined with LTE)
Having SIMs means nothing. Docomo UMTS uses a SIM that is incompatible with your "standard" SIM. In Asia, CDMA networks also got SIMs.