This is correct. The iPhone 5 uses a USIM only for LTE access, and the sim was only for LTE. In this version the phone would theoretically still work without a SIM, as it was activated by its serial number.
iPhone 5s, 5c, 6, and 6+ uses a CSIM, which activates and authenticates both CDMA and LTE- the same implementation as Verizon, and international CDMA networks. This was formerly known as an RUIM card prior to LTE days. These devices will not function at all without a SIM card, similar to its GSM counterparts. Also these phones gain the ability to switch between Sprint phones simply by moving the SIM card from one device to another. Once the unlock is approved on the 19th, you can also go to Verizon/AT&T/T-Mobile with no issues. You still can't take a Verizon phone to Sprint, though further reading proves this is something they're working on. Currently attempting to put a Sprint SIM into a Verizon iPhone produces an invalid SIM message after the phone tries multiple times to activate. Sprint white lists their IMEI/MEID to only allow "Sprint devices."
On another note, you can only take your Sprint iPhone to Verizon if you already have an existing account with them. They will NOT sell you just a SIM card. You CAN however start an account with a cheapie android phone and move the SIM over to your unlocked Sprint device or any other iPhone 6/6+, as they all have the CDMA bands in it, and it will work. The SIM card will tell the phone to "turn on those bands"