The glaring part to me is "without running it", since you can run it and still may never learn if it will ever finish.

To believe that to be a problem, it would require someone to think that saying "impossible in general to x without y" is the same thing as saying "doing y is sufficient for x". The thing about that is that they're not the same, and that kind of person is certainly in no position to be (loudly) trying to point out others' logical mistakes.

My take was that if you did run and it stopped, well, then you know.

Absent of any state change like input.

The emphasis of "generally" is poorly placed, but more importantly they also imply that you can tell if something halts by running it, which is only true if you run it long enough for it to halt! (Which is the real crux of the halting problem)

not a generous interpretation