What your lawyer meant was that its very easy to "pierce the veil" of the business entity (your LLC) to go after the owner when the business is owned and operated by a single person. In such instances, it is very difficult to show that the business has a separate identity from the owner. This is especially true for consulting, where the consultant is the business.

On the other hand, it is very difficult to pierce the veil of a business entity with more than one owner (unless the second owner is a spouse or family member of the first).