All the AGM batteries I've bought (YUASA motorcycle, small equipment) have shipped dry, and had to be activated before 'sealing.' FWIW, all have been imported from Asia, so there may be safety issues that preclude shipping them already activated.
Just because you can pry off a cap, doesn't mean the battery is not sealed. The liquid had to go in somewhere.
Chemistry is not quite the same as flooded cell lead acids, because part of the battery chemistry involves binding the hydrogen and oxygen from breakdown of water to a storage material, and that involves a small exchange of energy. The water level will fluctuate with acid concentration, as the battery is charged and discharged.
The worst you could do adding distilled water would be to add too much, forcing an overflow condition as water is restored from recombining gases stored on the mattes. Many AGM designs have some compensating space, or a pressure-relief venting system that prevents bursting the case.
FWIW, at one time most replacement automotive flooded-cell lead-acid batteries were also shipped dry, and activated by the installer pouring in the acid. This helped shelf life, when shipping was slower and retail supply lines were longer. Most of the batteries we sold, we added the acid and charged them, as part of the installation.
Once this practice became less common, GM's Delco division re-introduced the shipped-dry battery as a premium feature, battery guaranteed fresh because it is not activated until you buy it.
Up to about 10-15 years ago, replacement batteries were still being charged and tested by the installer at time of sale. I am annoyed that I am now being sold batteries off a storage rack, maybe six months sitting there, and being told "it is fully charged, was charged at the factory."