To be honest, for the longest time I thought 'fed by' meant just that. That if you attack an Element pet with an attack that 'feeds' its Element, the Element pets gets health back, cause the attacking element FEEDS the other Element.
Though we could always have Traits that could allow this, regaining health is hit by same Element (i.e., Fire pet hit by Pyro would regain 25% of Pyro's damage [so 1 point out of the 5 base damage]).