I think that
Flight Delay gives the correct summary: the airline is responsible to provide meals, refreshments and overnight accommodation. When restaurants on the airport are open, it's fine to provide meal and refreshment vouchers; but when restaurants are closed, the airline has to find another way to provide meals (at reasonable times).
I do assume that BA will have a discussion about this incident with the people that handle their passengers in Venice... Someone there erred in not arranging for refreshments an accommodation for the night. (I guess when rumour got to London it was too late to arrange something other than breakfast.)
For the lawyers, the relevant paragraph from the EU directive
Article 9 Right to care
1. Where reference is made to this Article, passengers shall be offered free of charge:
(a) meals and refreshments in a reasonable relation to the waiting time;
(b) hotel accommodation in cases
- where a stay of one or more nights becomes necessary, or
- where a stay additional to that intended by the passenger becomes necessary;
(c) transport between the airport and place of accommodation (hotel or other).
2. In addition, passengers shall be offered free of charge two telephone calls, telex or fax messages, or e-mails.
3. In applying this Article, the operating air carrier shall pay particular attention to the needs of persons with reduced mobility and any persons accompanying them, as well as to the needs of unaccompanied children.