My husband and I can't always consult each other on discipline. The kids know that they could get a different reaction from one than another, although we tend to be fairly consistent. We just take enough turns parenting that if we had to consult each other, nothing would get done (he works/goes to school, I go to school, and we're often home at different times.) The biggest thing is that, most of the time, we don't interfere with each other's consequences (although there have been times when one or the other has stepped in, but even then, consequences are still pretty consistent).
As far as grounding, I do think that it's appropriate that the consequence fits the kid as well as the misdeed, but I also think that 1 day's grounding is not bad, even for the most sensitive of kids. I would call it maybe slightly excessive, but I wouldn't argue it this time. Like you said, she'll live through it (and a day w/o tv/video games can be GOOD for her anyway!). Sometimes, it just takes something a little more for a kid to realize that they need to take a better look at themselves.
I would talk to him (alone) about what should and shouldn't be done for future instances like this. Come to some sort of agreement so he doesn't have to consult you. I assume you want him to be an equal parent. Expecting him to call you and ask you if he can impose a consequence undermines that, which in turn undermines his authority, regardless of if you agree with exactly what he does. That's the bottom line.