"Well, I have a microphone, and you dont. SO you will listen to every word I have to say!" - Adam Sandler as the Wedding Singer
Okay, I'll admit, having the microphone does not make the singer right, but there is practical application why I adopted this rule of thumb. It has to do with the fact that more attention is being paid to the lead singer, who happens to be holding the microphone, than anyone else.
There are exceptions to this rule and they pretty much fall on the drummer. Sorry bass players, guitar players, keyboard players, percussionists and banjo players. (Banjo is getting HUGE in worship right now. I'm surprised you didn't know that. It's so introspective and worshipful.)
If you start a song and the singer comes in early, then guess what... That's the new start of verse 1. Even if they come in on the wrong beat. Playing along and hoping they catch up is unlikely to work, and will become painful if it goes longer than 1.5 seconds. If they forget the words to the song and need an extra four measures, then four measures it is! Even if they jump to a bridge when it should have been a chorus. Someone's got to drive this train and whether you like it or not, the singer is in the driver's seat.
Do I say this because I'm a singer? No. Do I say this because I think the singer plays the most important role in leading the song? No, even though arguably they do. Do I say this because the singer has the most sensitive personality and we need to prop them up every chance we get? No, even though that might be more true than I'd like to admit.
There are times for collaboration and making decisions as a team. The middle of a song is not one of those times. The middle of a song calls for immediate, dictator-like decisions. Even if the dictator doesn't necessarily know what they're doing. And if this is the case, you might want to consider addressing that bigger issue, hopefully not in the middle of a rehearsal. Awkward.
Now, you may have a different philosophy and believe that everyone should follow the piano-playing music director. That's great. I think the most important aspect here is that your what-if scenarios are thought through and then communicated with the entire band so they know what to do when (not if) something goes wrong. Because eventually something will. Knowing who to look at for body language, hand signals or spoken cues before you are in that situation helps you pull out of a nose dive quickly.
I have to admit I don't worry too much about things going wrong in a worship service, and in fact, there are times I enjoy it. You learn a lot about people when things don't go as planned. Plus, no matter how bad us human beings may screw up the plan, church is gonna happen. I'm pretty sure God can handle a singer coming in at the wrong measure or having to start Little Drummer Boy half a dozen times because half the band forgot how to play it. Not that that happened to me or anything.