Is the document you speak of for taking the child out of the country or is it for medical treatment or both?
I took my 5 year old grandson to WDW last year (did not cruise). I thought I was so organized and was doing everything right.

I had a note signed by my daughter (his mother) authorizing medical treatment.
I knew by the time we landed in Orlando, the poor little guy was coming down with something.

I figured an afternoon at the clinic, right? The clinic we were taken to would not treat him (or even look at him) because the note I had was
not notarized. I was unable to reach my daughter by phone at that time.
Our only choice was the ER, where we spent the entire first day of our vacation. Hospitals will treat you without a notarized note, but the illness may not have escalated to the point it did (he ended up on IVs), if he would have gotten treated right away at the clinic, instead of spending from noon til 10 PM in the ER (we did not get seen until 6 PM! - yes, it was nuts. The whole story is in last years trip report).
Lessons learned -- get medical forms notarized. Use Docs On Call for any minor medical treatment while at the resorts.
Tink