Without any research, generally no. It is unlike what is formerly known as the Master-Servant relationship, employer- employee.
While at times the Master was responsible for the actions of an employee, called basically, Respondeat Superior, I believe this trend is outdated to a certain extent, of course, state specific.
Generally, the action would have to be within the "course and scope" of employment to impute liability to the Employer under a basic Law of Agency theory.
Third party agents are generally not representative of the hirer to establish a joint or several liability.
I can't be any more specific without research. I have read some cases in the past at the law library, but can not remember a definite outcome.
You can research some selected terms; Repondeat Superior; Law of Agency, + subcontractor; etc.