I talked about cross wound thread vs stack wound a year or two ago on my blog too. I find it can make a really big difference. In particular on machines that are very sensitive about tension - sergers, embroidery machines, long arms, etc.
I believe that humidity does make a difference but I think it's possibly "relative". The machine is usually serviced in the area that it's used. I think if it's set so it works "good" with threads at the time of service then of course sees the appropriate adjustments with a change of thickness or slipperiness of the thread,
most machines will soldier on just fine until there's a major change in humidity. Some may be a little grumpier.
Here's something to think about though - thread when it's drier is may be a little less slippery (or maybe more slippery, depending on what it's made of) and possibly even a tiny bit smaller than if it's holding more moisture. If you put thread in a bowl of water, I'd assume it would swell a little. This change in its characteristics might be just enough to affect some machines. It was an Elna owner's manual that first made me think about any of this. It mentioned that if you had thread breakage to put the spool in an open window over night. It would collect some moisture and regain its strength. Of course too much moisture could also cause issues as well, possibly even what's being mentioned in this thread.
I do know that Lucey (my long arm) has an absolute hissy fit which sometimes results in arguments between the two of us and one of us sometimes flounces off in a huff. I won't name names, that would be unkind. I can completely service her and change needles, tear apart the tensions, etc and still she'll be snapping threads like crazy. Stuff she was fine with the day before or even earlier in the day. The only thing that fixed it? Raising the humidity from 19% (no wonder I had a sore throat when I was working on her!) to 40%. Then she was a new girl and I felt like I needed to apologize to her for the nasty things,... uh,...someone... said about her.