Are you familiar the legal phrases "in evidence" and "not in evidence", as in "Objection! Question assume facts not in evidence!" or "Your honor, I move Exhibit A be admitted in evidence" or "You, the jury, may only consider the the testimony that has been admitted in evidence"? When you object to say something is "not in evidence", you're not saying evidence for it doesn't exist -- you're saying "You just started relying on a premise we haven't agreed to yet". That term of art might be confusing and a reason to avoid saying "not in evidence", but I didn't get the sense the article understood that sense of the phrase.
This post is a sequel to my previous smash hit, don't accuse your interlocutor of being insufficiently truth-seeking. Like many good sequels, I've mostly just reskinned all the same points with a slightly different presentation. This time, I argue that you shouldn't accuse your interlocutor of making arguments that aren’t rooted in evidence. This doesn't mean you can't internally model their arguments lack of evidentiary support and use that for your own decision-making. It just means you shouldn't come out and say "I think you are making arguments that aren’t rooted in evidence".
What you should say instead
Before I explain my reasoning, I'll start with what you should say instead. This depends somewhat on what your underlying issue with their argument is:
"Your evidence doesn't actually lead to your conclusion"
When you say an argument isn't "rooted in evidence" or something similar, often you just mean the evidence presented doesn't actually justify the conclusion. This can be because your interlocutor has misinterpreted the evidence, including by overestimating its strength, they have failed to consider counter-evidence, or many other iterations on this theme.
"Your theoretical arguments are wrong"
If the arguments offered by your interlocutor are primarily theoretical, you can simply say that these arguments are wrong.
Nothing
If your interlocutor offers literally no reason at all for their position you most likely don't even need to engage. Remember that this doesn't happen very often. If you think it is happening you are probably mistaking one of the above situations for this one.
You can also add your own flair to any of these options to spice things up a bit.
Why you shouldn't accuse your interlocutor of making arguments that aren’t rooted in evidence
Clarity
It's not clear what you are even accusing them of. "Not rooted in evidence" could arguably be any of the options I mentioned above. Just be specific. If you really think what you're saying is so important and nuanced and you just need to incorporate some deep insight about evidence, use the "add your own flair" option to sneak that stuff in.
Achieving your purpose in the discussion
The most common purposes you might have for engaging in the discussion and why invoking "evidence" doesn't help them:
You want to discuss the object-level issue
You just fucked yourself because the discussion is immediately going to center on whether their arguments are rooted in evidence and whether that accusation was justified. This may sound good at first, but it actually isn't. You've pushed the discussion towards a meta debate about what counts as evidence instead of the actual evidence for or against your interlocutors claim. You failed to follow the NEVER GO META imperative. It would have been better to just cut to the chase by going with option 1 above.
You want to discuss your interlocutor's misconduct
You again fucked yourself because:
Conclusion
Don't accuse your interlocutor of making arguments that aren’t rooted in evidence. Just say they are wrong instead.