I got the impression Wizards and especially Seers are extremely magically powerful. At least Tedd, who had dual powerful wizard parents, is likely extremely powerful. If magic inheritance is somewhat Lamarckian, or if being around powerful magic helps people develop magic that likely magics it even a bigger deal.
As for Tedd resisting the magic scanner, he did that because he was scared. He has enough magic resistance he can outright resist or dispel weak spells. Arthur and Edward may have the same ability.