I mean, it's not like they're mutually exclusive things. You can be an effective leader without being an asshole. The whole "tough guy" shtick is a lot more grating when you haven't really proven anything yet and the team is a perpetual gong show.
Like others have mentioned, there's been way too much noise around Cronin/Verbeek and the type of environment they seem to have created for all of this to be just a fart in the wind.
I agree but at the same time, look at the Tkachuk situation in Ottawa. The owner had to come out and state that they have never been in any discussions about trading Brady. This is not the first time he's had to do this. It still doesn't stop the rumors. Zegras is similar although less public support from the team/owners.
Right now, the rumor this season is that Cronin is awful to play for and Verbeek is rough around the edges. In that video, they clearly are just repeating what we've all been hearing all season and there was nothing new to report. Most of the reports are from last season and in the summer. I can't remember seeing any negative comments about how he speaks to players this season.
All that being said, IMO, Cronin should be fired because he has not been successful and there's a lot of evidence to prove this. Having a GM and coach that are both tough in how they communicate is probably not a good balance.