> I sure as hell can distribute binaries if I like

As far as I understood the argument, you're free to distribute binaries, you just can't call them "Signal", since it's a trademarked name (?).

You can't modify it and still call it Signal (i.e., misrepresent the trademark). You should be able to redistribute unmodified binaries.

Regardless of whether you actually should* be able to, "should" and "can" don't always match.

* I'm sure Signal would object to you redistributing binaries under their name, even if you claim they are unmodified, but they can't verify that fact. And honestly such an objection seem pretty reasonable.

Modification of binaries of open source projects is a common and perhaps the only issue from a trademark standpoint. Firefox and debian used to have this too until they resolved it at some point.

I think the point is that you can't call it Signal. Is that correct?

Yup, also can’t really prove it came from the same source code.

What is GNU IceCat (formerly IceWeasel) then?

Firefox's license did not permit use of trademark. Eventually an exception was made, and now GNU IceCat is mostly a relic.

Signal's license on the other hand, does permit use of trademark. If nothing else this means that using the DMCA for this is wildly inappropriate.