Part of it might have to do with the matter of some SSRIs inhibiting CYP2D6 and hence increasing Dextromethorphan levels. if I remember correctly normally DXM is metabolized by CYP2D6 to DXO which is not a SRI but is still an NRI, so if you inhibit CYP2D6 you would get more SRI effects because you have mostly DXM.
I'm sure that a fellow bluelighter Dopamimetic would have more to say on this matter but it might also be that DXM does a whole lot of things while SSRIs are typically only selective for the SERT. DXM is also a sigma agonist and sigma is a kinda weird receptor, maybe it would contribute to serotonin syndrome or at least over dose effects. NMDA antagonism could lead to increased excitotoxicity but that would be more with the SSRIs that do not inhibit the CYP2D6 (Dextromethorphan itself is not very strong as an NMDA antagonist, it's DXO that's the real NMDA antagonist, and once again it's the liver enzymes that make the DXO) so you would likely get more NMDA antagonist related toxicity and less SRI related toxicity from combo of DXM with a SSRI that doesn't inhibit 2D6.
I do wonder if DXM is really that bad to combine with SSRIs or if it's just a general opinion going around because there are warnings about serotonin syndrome on the bottles. There are definitely case studies of DXM abuse and SSRIs leading to serotonin syndrome though. But I wonder if that's mostly with the CYP2D6 inhibiting SSRIs.
I would like to say that NDMA antagonism itself doesn't induce excitotoxicity while the antagonist is active, only as a "rebound overexcitation" when the antagonist has left the system, so in the case of concurrent use of SSRI and DXM that would not be the case. Moreover, I think it is still not clear to what extent NMDA antagonists actually induce excitotoxicity, especially following just one use (correct me if I'm wrong). NMDA antagonism would actually decrease the risk of excitotoxicity while the drugs are active.
I think the more probable reason is, like you said, just stereotypical thinking. Also, is it really considered that SSRIs are safe in overdose? I'm not an expert on SSRIs, but I think regardless of what the substance is, if it inhibits serotonin reuptake, then it has the potential to cause serotonin syndrome. In any case, if anything then I think Cotcha is right about SSRIs inhibiting CYP2D6 and thus indirectly increasing DXM's SRI action. But most likely it's still safe to take them both at the correct dosages (not that I advocate trying that, as always you never know what might happen).
There are many misconceptions about combining drugs. For example, a lot of people believe that drinking alcohol while taking antibiotics is an absolute no-no. It is true for some antibiotics, but in most cases there are few interactions if any. I have drunk while taking antibiotics myself (researched beforehand of course). Another one is alcohol + paracetamol. While it is true that the risk of serious hepatotoxicity increases when combining those two, it's illogical to say that combining them in ANY amounts is dangerous. People tend to over-simplify things that they don't understand very well, so they tend to think that if a certain combination CAN be dangerous (APAP+ethanol; antibiotics+ethanol; opioids+benzos) that it follows that combining the two IS dangerous.
Also, there are probably a lot more cases where persons co-ingested dangerous amounts of DXM and an SSRI compared to overdoses of SSRIs alone, so the latter is just not thought about much when serotonin syndrome is brought up.