Best repeatable example of this is tobirama in the group instance, his skill usually goes off before the icon even flashes above his head. When this happens, regardless of initiative bonuses, you do not get a chance to stop his skill even though your interrupt (like iruka) may be in position 1 and have priority over tobirama. The only times I actually get a chance to interrupt him is when Sakura uses her ability the same turn and gives you a chance to execute your move.

Yeah some players are just really good at their timing for moves.