Technically, a "safety" describes designs and mechanisms by which a firearm discharges if and only if the trigger is pulled.

Colloquially, the word is often used to describe an external safety that must be manually disengaged (otherwise there is no bang even if the trigger is pulled). However, in modern firearms, even those with external safeties also have internal safeties that mean that even with the external safety disengaged, if you dropped the firearm or hit it with a hammer or something, it would not fire.

As others commenters have said, in the case of the P320, the claim is that it would fire without the trigger being pulled; and in the specific case of the airman, it is further claimed that there wasn't even a precipitating physical shock like it being dropped or hit.