The singer said it well, and for all to hear: "You can always tell when the drummer's bored."
He's right. It's easy to tell when a drummer is bored. It's when he/she throws in all kinds of stuff that isn't relevant to the music. It's a different sort of thing from merely being too busy or not being faithful to the style. You can overplay and yet still be working hard to make good music. The bored drummer, on the other hand, tries to generate some excitement when it's completely uncalled for. You can often tell from the drummer's facial expression. It's one of attention seeking, looking to the band or audience as if to say, "Did you notice me?"
Is there a cure? There is, and it's surprisingly simple. Just remember why you're there: to combine your efforts with those of the rest of the band to produce quality music. You are there to serve the music, no more, no less.
Not appropriate for the style?
One reaction to an unfamiliar and possibly uncomfortable situation is to disallow all knowledge and interest in the subject. So you play what you feel like playing rather than what's right for the music. Say you're a thrash metal player and you've landed a fill-in gig with a blues band. I'm sure you've played plenty of blues before, and you've likely heard enough authentic blues to be able to mimic the style if you give yourself permission to do so.
I find that the core rhythm can always be found in the music. While I may not know a tune or even the genre, the rhythm always forms the foundation of the tune and all I have to do is listen for it. If you find that you’re not clicking with the genre, a bit of homework and listening will pay off.
You’re distractible?Ah yes, the ADD problem. The interesting thing about people with ADD is that they typically put a lot of effort into overcoming the difficulties that accompany the condition. The frustrating part of ADD is not the inability to pay attention but the inability to control it, to make it do what you want. People with ADD can attend just fine, right up until the moment their thoughts shift to something else with no warning and no rationale.
One trick to living with this peculiarity is to keep progressing. Always look for the new and novel, which all music contains if you take the time to look for it. It's important to be as stress-free as possible on the gig. This is critical for someone with a wandering mind. It's also a good idea to have reminders available, so charts and notes might be a worthwhile addition to your setup. If you happen to be the distractible type, use whatever coping tools that will help you keep on track. (By the way, ADD and just not paying attention are not the same thing.)
You’re truly bored?One of the main reasons drummers overplay is because they're bored with the music. In my experience, boredom comes from within. If you crave excitement, that's a choice. You can also choose to crave a challenge. There are potential challenges in every musical situation. Can you play it more authentically? More empathically? Can you hold the time rock steady? Can you pay fills only at the end of complete phrases? Can you play fills that are shockingly simple? Can you follow the dynamics of the tune throughout the volume spectrum? I find I'm never bored when my objective is to do a better job and to always improve what I'm doing.
And if you're simply bored, either get un-bored or step aside and let someone else have a go.