Can a freelance be loyal to the employer?

It sounds as oxymoron. In the case of hiring a project manager, this contradiction of terms is lessened by the nature of the matter. By definition the project is a temporary (citation needed) situation.
The forming organization that will be dedicated to the project is part of (or has an important relation with) the company. The allocated resources are people who have much seniority of their temporary boss.
This is the first peg to be mounted on, assuming that the whole process of delivering a successful project resembles to a steep ladder. Going on with this analogy, there are some basic checks to be done before starting. Is the ground is firm enough? This means that the project’s scope and the derived mandate (as described in Prince2) are clearly stated and are accepted by all stakeholders.
Senior managers are, among the stakeholders, the most committed to this mandate. It is the result of their decisions.
Now the required fidelity has found a more tangible object. All people working at the project can share the same aim.
With a clear target, leadership can be exerted with much more efficiency. Now the staff management can be focused on the single person needs and expectations. The art of leadership can be defined as the ability of directing each person’s energy toward the same goal. This is reached when people are convinced that their personal needs and expectations will be satisfied by reaching defined objective.
An example of this: successful projects are big badges to be worn.