Being loyal to a corporation is unhealthy. It has a poor foundation. They are created to drive profit and promote their interests. Not yours.
It is healthy, if applicable, to identify with the goals and mission of the corporation. But we should not find our identity in it.
Now when talking about the people in a corporation, well, they can be your advocates. Your champions. Being loyal to a solid manager or leader can be a launch pad. A library of wisdom.
When challenged with where to put your loyalty, put in in people and not the corporation.