^UPDATE: In light of everything we've learned in IG's impeachment trial, I think that the above statement needs clarifying.
Regardless of what any Constitution says, Owners have the right and obligation to enforce the "implicit Constitution" of IMGFLIP_PRESIDENTS, which guarantees things like: (1) Imgflip TOS is followed; (2) Elections are free and fair; (3) Presidents don't start being blatantly censorious, rude, and abusive to the community just because they feel confident the government has their back.
IF Congress is reformed to be actually reflective of the stream as a whole, then my comments above would stand, and I don't think the Owner should generally be involved -- but as it stands, there's a glaring gap between Congress and public opinion, as surveyed in many strawpolls that have been taken this term on subjects like the Bank and impeachment.
IG's modding and conduct has brought him right up to the line of where the Owners could be justified in removing him as Mod, regardless of the impeachment process, in my opinion.