While technically a different device, I think you have the right concept.
I recently had another conversation with yet a different Straight Talk rep. Though every single one says something different, this most recent "reason" I don't get 4G makes the most sense thus far. According to the rep, my device is not accessing the 4G network because I do not have a Sprint SIM card in it. I've come to find that's really the whole purpose of the Sprint SIM. Had I been a Sprint customer, I would be seeing the same lack of 4G with no SIM. I haven't gotten around to it, but the general consensus of the internet is that I have the best chance to obtain one through Sprint's International Customer Support (despite not being a customer or international).
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Why do you say that? Is that a hardware limitation of this particular variant, or a limitation of Straight Talk's stupidty? I had an Verizon Galaxy S4 getting 4G on Straight Talk's GSM side. I gave the phone to my gf and she was getting LTE on AT&T. I know, again, technically different devices, but close enough to speculate.