Nope, if they screw up their conduct as a lawyer, that's their problem. It's the same as paying a contractor to build a building for you. You get the outcome, but if in the process the contractor gets drunk and beats up one of the construction workers, he gets in trouble, not you.
There is a wide gap between paying for a service and hiring an employee to work for the company.
There is a wide gap between paying for a service and hiring an employee to work for the company.