@PhilipD I defer to your clearly greater expertise. :-) Seriously.
Re: Snake oil. I don't know what the quality of the output of these commercial small UPS's is like, I haven't measured it, hence the "if" in my earlier post. So if the output happens to be clean anyway, then obviously there's no issue.
A second point is that the signal voltage I get is really really low, <= ~ -65dB d/s attn., so any noise, if present, would be a big deal, whereas for normal users with shorter lines, the same noise input would not be significant. So aside from your good points about the filtering capabilities in modems' cheap PSUs, I should have qualified my earlier post with a comment concerning long lines.
So lots of caveats need to be appended to my earlier, hasty, post.
It may be that the improvements I saw when fitting filtering devices were a red herring, non-reproducible, and were just down to the vagaries of what sometimes happens to your sync rate when you power down and up again. For reasons poorly understood, I do occasionally seem to get an improvement in downstream sync rate just by forcing a resync when a link has been up for many days.
The link to that controller for an SLA battery is very interesting, seeing as I don't get a run time that is anywhere near long enough from my current inexpensive UPSs. Many thanks for that.