[Phanx]

Search your addon files for "RequestTimePlayed", which is the function that gets that information. Any addon calling that function to update its records should also hide it when it wasn't requested by the user. Here are the relevant bits from Broker_PlayedTime; feel free to point the author of Altoholic at this thread for copypasta.

local requesting

local o = ChatFrame_DisplayTimePlayed
ChatFrame_DisplayTimePlayed = function(...)
	if requesting then
		requesting = false
		return
	end
	return o(...)
end

function addon:RequestTimePlayed()
	requesting = true
	RequestTimePlayed()
end

function addon:TIME_PLAYED_MSG(timePlayed)
	-- do something with the timePlayed here
end