Yes you're right.
I take the point that if the club feels a decision is attracting heavy criticism they might want to clarify their position or give further detail, but do it through an official release, or at worst an official Notts County FC tweet. Every time Alan engages in these debates through his personal Twitter he's inviting more flak upon himself, which I actually don't want to see because eventually it will sour him like it did Ray Trew.
One advantage you have as a football chairman (as opposed to a football manager who pretty much has to accept a high profile) is that you don't have to say too much. You have the ultimate power to make decisions but you can do it in the background and allow the attention (be it praise or criticism) to focus on your football professionals. I've said it before, but Steve Gibson at Middlesbrough has shown how it's done, hence his longevity.