All you're ever going to get is anecdotal evidence...based on the limited number of guns any of us see at our local ranges....and even if the Rugers we see do fail often ...none of us has any idea if or how well they were maintained / or if they were mistreated...that may have contributed to the failures. Absolute proof....isn't going to be there..../ we will all have to settle for what we see - and hear from shooters.
In my area....if you are perusing the gun racks at a local club shoot for Trap, Skeet or Sporting Clays.../ in my opinion, the number of Ruger shotguns you'll see ....( out of 100 O/U shotguns say ) ...will be 5 or 10 at the most / Rugers are not widely used even at casual club events / and the more serious the tournament...regionals, state tournaments, etc... / the less of them you will see around the event.
You'll have to ask yourself why that is ....but in my opinion, if they were holding up, and shooters were hearing they were holding up pretty well ....you would see a lot more of them / because they're relatively inexpensive compared especially to O/U's like Browning and Beretta --- and you'd see guys buying a few of them for young shooters, etc..
In my area...Trap shooters are a little different / but you won't see hardly any 28" or 30" barreled O/U's among serious Trap shooters...( 32" barreled O/U's are common / or 34" singles )... Browning, Beretta, Blaser, Perazzi, Ljutic, Kolar, Krieghoff make up at least 90% of the guns I see - with the bulk of them being Browning or Beretta.
Skeet .../ and sporting clays - you'll still see some 26" and 28" barrels / but 30" barrels are common...and Browning, Beretta, Blaser, Perazzi make up the majority of guns I see...but there are always a few Kolar and Krieghoff as well...especially in full length tubed guns.
Now I'm not saying all the guns I see are higher end Browning or Beretta's ...I still see a lot of Silver Piegon Berettas or Lightning model Brownings...especially among new or young shooters.....but I see way more gas operated semi-autos (mostly Beretta ) that will far outnumber O/U's from Ruger....as entry level guns for new shooters.../and guys buy them for young shooters because they're a lot of gun for the money as a learning gun for new shooters.
All of the Rugers I've seen at my local club....were brought out by casual shooters.../ not guys you see every week....
But proof ....no, you aren't going to find any /... any more than the anecdotal evidence you cite based on what you see in your leagues, etc...its all anecdotal.