In short, the buck stops with the EC. Yes, they are supposed to elect those office bearers from among their number (one EC member can have more than one executive function). Yes, the treasurer is responsible for those financial matters but the rest of the EC is responsible to oversee the treasurer and ensure that the treasurer’s functions are performed. So, the whole EC is responsible.
If the keeping of accounts is delegated to the strata manager, they should make the accounts available to the EC any time the EC wants to see the financial records. Ultimately, the buck stops with the EC.