Is this always the right way to play? Not necessarily. There will be times when you'll have to handle things a bit differently. Perhaps you're teamed with a bass player who doesn't lay down a solid line. Or maybe someone in the band just doesn't connect. In either case my recommendation is to work with the strongest or the weakest player.
Here's what I mean.
Let's say you have a strong singer, much stronger than the others in the band. If you 'marry' the singer, the two of you will then form a solid team that can create a good foundation, and that can help pull things together.
The other situation is a bit trickier. Say you're backing up someone who is sort of all over the place, and providing solid time just isn't working. The solution is to marry this player. Sorry to say, the person most likely lacks the ability to effectively work with the team. So your best option would be to play as tightly as possible with him or her. Then you become a sympathetic anchor for that player. You also become the guide for the rest of the band, and the liaison between the band and the ‘loose cannon’ in times of distress. If something odd happens -- a bar of three perhaps -- you can catch it and communicate it to the rest of your team with the offender being none-the-wiser.
Now, I happen to have done a fair amount of this sort of compensating for assorted musicians and their varied approaches, and I don't mind admitting that I'm pretty good at it. But I would far rather marry a good bass player. Just sayin'.