the data behind these statistics are so riddled with bias that I am extremely dubious about them, to the extent that I think it'd be epistemologically safer to largely disregard the stats

This right here is what I'm arguing against. I'd go so far as to say applying this at a macro level is dangerous and destructive (and let me be clear I am not accusing you of doing anything dangerous or destructive, this has been a lovely conversation and I hope I carry no offense. A politician saying this would scare me, but talking about this in a small setting is interesting and productive).

What I have seen from your argument is the possibility for bias at a few different levels of hypothetical data. Now again I'll caveat that this is not my area of expertise and I'm probably not doing a great job representing the body of literature, but let's examine a few studies to hopefully demonstrate what I mean. In this study accessing women's arrest rate for violent crime there are some interesting charts that help illustrate my point (which is largely unrelated to the focus of the paper). They came up with this set of graphs:

I'll grant that these partially illustrate your point (the part I said I agreed with), the arrest rate for a crime is not necessarily tied to the act of doing the crime itself, and it does so by comparing victim reports of crime with arrest records as a victim report has nothing to do with if an arrest is made or not. Now you could also say that maybe it is less likely that a victim of a woman committing assault is less likely to report they were victimized along with them less likely being arrested. Sure I could even get behind that, but does that account for the 10-20 fold difference in both of them? That would be wild.

For an ever clearer example of this let's look at another citation (shared author as before) looking at gender differences in drunk driving. In this analysis it was found that 30% of self-reported drunk drivers are women, 25% of DUI arrests are women, and 18% of legally intoxicated drivers in fatal crashes are women. Here we would need to come up with an explanation that up to triples the "real" counts of DUI driving for all three of these stats. We'd have to say well women are 2x less likely to self report than men (why?), they are 2x less likely to be pulled over for DUI (maybe because cops don't target them as much?) , and that they are 3x less likely to cause accidents that result in death (I guess they are just better drunk drivers by a massive margin).

Even if there are potential for bias in the data you can then account for it with other studies, for the last point the cleanest way would be to ask "are women better at driving under the influence than men?" and a study that tried to tackle exactly that found that "women displayed greater impairment than men on all behavioral tests and also reported higher levels of subjective intoxication compared with men."

Sure we could poke and prod at hypothetical biases in this data but just because you can generate a plausible explanation for bias doesn't mean you should "largely disregard the stats". The reason I claim this is dangerous at the macro level is because this is how you get climate change deniers, vaccine skeptics, smoking and lung cancer deniers, and on and on. There are times where it is appropriate to raise eyebrows at statistical findings, but with something as clear cut as violent crime with men vs women it is not it.