You are on very shaky ground with this line of argument, which attempts to cast aspersions at basically all of psychology because of controversies unrelated to the the issue we're actually talking about.

Yes, there are questions about whether playing "Mature"-themed games actually causes problems for teenagers.

Yes, there is an effort, probably ill-conceived, to restrict access to "Mature"-themed games for teenagers.

We are not talking about teenagers; we're talking about a 4 year old.

One simple axis of argument to observe here is the Harvard (Kutner & Olson) vs. Iowa (Anderson) debate; Kutner's book points out that much of the psych research is methodologically flawed. But both Kutner and Anderson agree that exposure to very violent games is associated with increased aggression. Kutner just doesn't want to see all games demonized for all pre-adult age groups.