You can get consistent results modelling a random process. For instance, if you have a very small sample, you might "luck out" and get consistent results. If you have a large sample you'll get consistent results because you'll approximate the true distribution. In either case, the process remains random and you're only modelling noise.

One kind of research bias is p-hacking where you basically mine your data for spurious correlations and only form a theory to explain the correlations once you find them. The problem with that is that, to paraphrase the philosopher, if you look hard enough into the noise, the noise turns up correlations. You can always find a signal if you look hard enough.

(I think this is a better answer- sorry for the multipl edits).