I rarely have issues with Discovery tickets - the vast majority of smaller operators are used to them, although I have had a few Arriva drivers who question them if they see an independent's logo on the top. I think the biggest issue is that Discovery tickets are the only tickets that don't have a QR code and don't scan, so it's tempting to think it must be suspect.
Likewise, I find most operators quite happily accept them - even if, as you say, the ticket has the "wrong operator" printed at the top - but the one operator I have consistent problems with is Diamond Bus South East.
My current job has me working all over the place, but my commute almost always begins with buying a Discovery ticket on a Stagecoach bus (much better value for the journeys I have to make).
Whenever I have to board a Diamond Bus using said ticket (with the Stagecoach logo printed at the top),
every single time I'm met with utter cluelessness, and more often than not quite frankly appalling attitudes from drivers who tell you to your face that they (and I quote one driver) "do not care" to be educated on the validity of tickets and insist that I'm on the "wrong bus" and that I should get off.
Granted, I have come across a handful of lovely drivers on Diamond Bus, who - although clueless - were more than happy to take some friendly advice on Discovery tickets, one even admitting he'd never sold one before(!) - but the disappointing truth is that most of my journeys with them have had to begin with a dispute about ticketing, and that honestly makes me rather reluctant to use Discovery tickets (as useful and fantastic value as they are).