Yes there is a board, elected by members. But a technically democratic form does not necessarily translate into actual functioning owner democracy.
My experience after many years in the co-op world, is that the consumer owners of consumer co-ops - as opposed to producer owners of producer co-ops, and especially worker owners of worker co-ops - generally become disengaged from their ownership responsibilities as the consumer co-op grows larger.
For perhaps the most extreme example, REI is legally a consumer co-op. But with millions of owners in dozens of cities, how many of those owners even understand that they are truly the legal owners of the co-op? How many vote in board elections? REI's governance has been revamped to the point where member quorum for an election has been reduced to just 1/2 of 1% of the owners. And then, how many REI owners who vote have any idea what the actual issues on the board are, or what direction the board candidates actually intend to take the co-op?
The US food co-ops are nowhere near that large, but with tens of thousands of owners at the more well-established food co-ops, most owners like their store, but remain very distant from actually monitoring the board or getting to know the directors. Quorum for an election has been reduced to 5% or 3% of the owners at numerous successful consumer food co-ops.
So while indeed the technical structure of co-op owner democracy exists, in practice almost no member-owners of the larger food co-ops actually engage seriously with their responsibilities as business owners. The stage is set for the mainstreaming of the management of business operations. And with "growth" the new mantra in the food co-op sector - and with the same increased risks of liability for boards that actually direct their managers, rather than simply accepting monitoring reports from their managers - the incentive for directors to move toward strong, empowered management is high, with some co-op groceries now calling their General Manager the CEO rather than the GM. And at my co-op, the GM is now the board chair.
Worker owners of worker co-ops are in a much different situation. Not just engaging with the business they own as occasional shoppers, worker-owners engage with the businesses they own for dozens of hours every week, directly interacting with the business's managers on a regular basis. And instead of relying on their co-op as a nice place to buy healthy food, they rely on their co-op as their source of livelihood. So the level of engagement of the owners at worker co-ops is generally way higher, orders of magnitude higher, than at consumer co-ops.
And yes, if i had not had to run off, i would have added the point that corporate boards often simply appoint board members themselves, with no shareholder role at all.