Imho, this is invalid for two reasons : one is that "biologically meaningful" is not a well-defined term. Since it is not well defined, it can be confused with with "results that confirm the hypothesis we want".
Second, even if it were possible, the division of all possible cases into "random noise", and "biologically meaningful results" is a very gross oversimplification. Results can be partially meaningful, partially random noise. If one fits the model to the specific data at hand, and then checks for meaningfulness of, one cannot be sure what percentage of the data is random noise, and what percentage is biologically meaningful.
Regarding the possibility of validation through other means, that is always worthwhile; but that means one should treat the results one already has as exploratory data analysis, and not to use terms such as p-value when reporting its results.