Responsible in a management sense yes but not technically liable for a debt. There is a massive difference. The classic example is Chelsea and the loans backed by Roman Abramovich, he backs the loans as has full and total control - it is bassically an alternative to him putting the cash in directly. Either way it is his club and his money to lose. If the fans were able to vote him out with that debt still in place it would be a non starter.
Barcelona is not like Chelsea, it is owned by the members. Ahead of running for Presidency, the board must contractually agree to assume any fiscal imbalance they incur during their mandate - this board (Along with Rosell) actually amended the bylaws to ensure that fiscal balance was adhered to. In one sense to protect themselves and in another to provide the structure to operate & be 'transparent'.
Barto did not anticipate the motion to censure being successful which is why he never reacted sooner and why he tried so hard to thwart a vote over past several weeks. Now, before he exited he tried to cover those debts with deals he will likely argue were done to 'save the club' (Rather than himself).
Nevertheless, assembly of members will never approve these deals and it will all end up in litigation. So, yes the devil & his minions are out but the story is far from over in terms of financial health of the club. It's the first step and it's a significant one because no telling what he would've tried to stick the club with otherwise