Well the first rule should be looking skeptically at someone whose "analysis" involves something their core business provides/sells. Facebook and Google have been pushing data driven narratives about how effective their advertising is, and yet as a data scientist working at a large Fortune 500 company, we never were able to show meaningful impact anywhere close to what was claimed. This was met with pushback, as before my team was created the company relied on external analytics vendors who always came back with results that were magically what everyone was expecting/hoping for. But when my team tried to recreate what they had done, they would withhold information claiming it they were "trade secrets", or what they did provide was riddled with egregious errors.

I actually think that is the biggest argument as to why every company should have some kind of data science team. There is certainly important predictive models and analytics to be done, but the most consistent ROI would be to keep the company grounded and not dropping huge sums of money on the trendiest snake-oil analytics/AI solutions being hawked by vendors.