I wouldn't assume that. Although every cruise line is going to say "Safety is our #1 priority," they sometimes make other decisions when they see fit. The Costa Concordia disaster is a perfect example. At the time, the muster drill was required to occur within 24 hours of initial departure. Well, what happens if disaster strikes during those first 24 hours? It was quite predictable: many passengers won't know what to do. On the Costa Concordia, many passengers reported that they didn't know where their muster station was when told to report to it, and some didn't even know what a "muster station" was so they didn't even know what they were supposed to be looking for.
Common sense tells you that the muster drill should occur before the ship leaves the dock, yet that was not standard practice in the industry. And, the Costa Concordia was operated by a subsidiary of Carnival Cruise Lines, so it's not like it was run by some rogue operator that cut corners that the main lines wouldn't. Why were these drills not done before sailing? There had to be some reason, such as convenience to the crew or passengers, or cost. In any event, whatever the reason was was put ahead of safety, since had safety been #1, they would have occurred before departure.
Only after the Costa Concordia disaster did it become accepted practice that the muster drill occur before the ship leaves the dock. So, the notion that the safety organizations or the cruise line are not going mess around with safety was proven incorrect less than a year ago.
Having said all of that, I feel quite safe on the Disney ships. But I don't think it's unreasonable to ask questions.