I fundamentally agree that a "good" statistic is valuable because our eye test is, almost by definition, flawed.
The bolded part is what I disagree with, or at least disagree with for every advanced stat. To me each individual advanced stat has to be "proven" as something that actually accurately measures the quality of a player.
This is where the analytics community in baseball succeeded back about 20 years ago... they proved that team OPS (Oba plus Slugging %) correlated strongly with runs scored and that the legacy stats like BA, runs scored, RBIs did not. They were also able to go further and fairly accurately predict a teams offensive output based on the OPS of the roster.
To my knowledge (please correct me if wrong), no one in the hockey analytics community has "proven" any of the advanced stats in this manor.
So when I see a stat that claims a very bad player like Chiasson is actually good, my first instinct is to question the stat (or the data that feeds it).
Well, I don't think I can answer that question unfortunately, I'd be prompted to say that it hasn't been proven to that extent but looking at different stat will definitely help you find some good information.
If you look at Corsi, you'll find that, per example, Wiercioch has always been fairly good in that regard and that is because Wiercioch is good at making a first pass, most importantly exiting he zone which rushes the attack. By rushing the attack, we have the opportunity to have more shots generated than the opposing team since we don't get hammered in the Dzone.
Now, is Wiercioch a quality player outside of that? That is a totally different question. Like I said, these stats tell us something but they have to be taken into context, I wouldn't take Wiercioch over Methot because he has a better corsi per example. A lot of things need to be taken into consideration to have a real legitimate evaluation like quality of opposition, quality of teammates, shots generated vs generated against, scoring chances generated vs against, goals scored vs scored against, 5 on 5 impact and etc. There's not 1 stat that will tell you the whole story, I don't believe there will ever be one that will do that but it's something that isn't ingored anymore by most pro sports team for a good reason IMO.
These stats don't necessarely claim that Chiasson is good, they say 1 thing about his game while there is a lot more to look at but again, it does tell something.