Isn't there some issue with iPhones not being able to do data and voice at the same time on Verizon?
Yes. The iPhones that are CDMA/EVDO only can't do voice/data simultaneously because it's not in the spec.
The iPhones that have LTE can't do voice/data simultaneously because the iPhone only has two antennas and it reserves the extra one for receive/transmit diversity. Most other LTE phones on Verizon have a third antenna to handle just the LTE connection while a voice call is connected.
Similarly, the GSM iPhones can't do voice/LTE data at the same time for the exact same reason. However, simultaneous voice/data is in the HSPA spec so when the iPhone falls back to HSPA to make a phone call, you can still do data, albeit slower than if there were a third antenna just for an LTE connection.