Does your module maybe have a built-in VRM? The datasheet said the operating voltage range was 2.5-3.6V. A LiPo battery has a nominal voltage of 3.7V and a fully-charged voltage closer to 4.2V. That's definitely out of spec without a VRM.

It doesn't, but it's very tolerant of 4.2. I think the most I've run it with was 5V.

I absolutely believe it works for you, but I wouldn't ship that to customers, and I wouldn't expect what is ostensibly an authoritative reference tool to recommend it at all.

I’m with you on not shipping out-of-spec designs. Maybe this is a good place for a reverse-polarity protection diode!