This is the type of concern that I have a lot.

Using simple examples, we show that unmodeled effect heterogeneity in more than one structural parameter may mask confounding and selection bias, and thus lead to biased estimates. In our simulations, this heterogeneity is indexed by latent (unobserved) group membership. We believe that this setup represents a fairly realistic scenario—one in which the analysts has no choice but to resort to a main-effects-only regression model because she cannot include the desired interaction terms since group-membership is unobserved.

https://www.ics.uci.edu/~dechter/papers/19_embed.pdf

I am fairly certain that if this problem occurs I would not capture it. I check for the basic violation of assumptions, but only those. And of course that is one of many many violations I have run across in my reading. Which raises the critical question, is it useful to run statistical models when you are not truly a statistician. Because you may generate bad results due to issues like this and never know it...