This question has been brushed on, but not entirely answered. In refering to the maltese cross I’m speaking of either the real maltese cross which is four separate parts, or the more common iron cross commonly referred to as the maltese cross.
In attempting to find the origins of the cross I’ve found two different stories.
While the Flags of the World site is a collection of contributions, often by amateurs, they are serious amateurs who are open to criticism and correction. I would generally trust something found on the FOTW website over some oft-copied anonymous glurge that has been “borrowed” by numerous firefighter pages, (however well-intentioned).
Note that the Maltese Cross is not the same as the Iron Cross (separate image) which is actually a variant of the Cross Formée. Now, the Germans did, indeed, issue a medal in the form of the Maltese Cross, however, that medal was the Order of the Pour le Mérite (loads slow with frames) which was a separate medal from the Iron Cross. The fact that various German princes (both medals have history prior to the creation of the nation of Germany) issued two separate medals for valor or service that each incorporated a cross has, I suspect, led to the confusion.