Does it matter who orders the abdominal scan, the specialist or a family physician, whom i consider incompetent?

Probably not: First, you may want to try to resolve this lack of confidence in your family physician or find a new one. It is important to have a good relationship with your primary doc. That said, there are established appropriateness criteria for ordering certain imaging tests, and most centers/insurance companies require pre-authorization to confirm that the imaging test is truly indicated.