I'm sure Cid has some sort of overall "ownership" of all three Gardens, but he delegates leadership of each individual Garden to someone else. Martine was only the headmaster, not the proprietor or whatever. Edea essentially forced Martine out and took control in a coup of sorts, so it's not like Cid could've stopped it.
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"So cold. I am always by your side."
"There ain't no gettin' off of this train we on!"