I call BS.
That does not sound right. The phone is covered under warranty by Apple. Whether it's through T-Mobile/Asurant or Apple itself, ultimately it's Apple that takes care of it.
I'd talk to a different rep.
Take my advice as you will however. I've only been on T-Mobile for a month (ported over from Sprint) and I am making assumptions. I don't believe I am wrong but I could be.
When I was on Sprint I had an iPhone on lease. I shattered the screen and went straight to Apple. All I needed to do was an online ESN swap of the IMEI with my then Sprint SIM card serial number.
In the T-Mobile reddit this question has been asked before and people have been advised that all they need to do is call T-Mobile with the new IMEI.
Which is why I think the rep is lying to you. For what reason I don't know, but maybe they are simply misinformed. Ultimately, if T-Mobile gets back the same phone in the same color/capacity in good condition, why do they care? In fact, due to Apple's replacements they are likely to get back a better phone than what they gave you originally.