First you need to understand that your rights are different in a co-op compared to a condo. With a condo, a specific unit is transferred via deed to subsequent owners. With a co-op, you own interest in the entire building with rights as afforded by your contract. In effect, you are a tenant with the co-op being your landlord. You own interest in the co-op entity.
Due to that, what the landlord/co-op board can do is not based on your ownership rights of your unit (although even in a condo the board may have a similar right to demo your ceiling to investigate the issue. Even with a condo it could be based on the condo rules in place) because you do not own your unit. You live there based on a contractual right based on your shareholder interest held in the co-op entity.
So, what is fair matters less than what rights the co-op board has as provedided in the co-op rules.
In a realistic view of the issue, it may be easier to find the leak by opening your ceiling. It generally affords a better view of where a leak is originating than guessing and tearing apart a bathroom only to realize you need to demo more to follow the water back to its source.
Then, in a cost versus benefits basis (you need to look at your rules as to why this reslly is beneficial to you to as it is likely a cost born by the board and charged against the cumulative co-op fees) it is likely less expensive to open and then repair your ceiling than to tear apart the involved bathroom. In short: bathrooms are expensive rooms to rebuild. Ceilings are about as inexpensive as you can get unless it is some extravagant style.