I'm guessing the parent was asking about refilling due to the active ingredient expiring, not after an actual injector use. Hopefully most people who have epi-pens have to replace them due to expiry rather than due to frequently having to use them.
Replacing the pen after actually using it seems entirely reasonable - if nothing else, the needle will be contaminated.
> My understanding is the medicine in these epi-pens is fairly inexpensive..
an ampule of 1:1000 epinephrine is about $4. At least that's the price we pay for them on the ambulance. I'm a Paramedic in the US, and we took the Epi-Pens off our units ages ago due to the ridiculous costs. Now we just draw up epi by hand with a typical insulin syringe and deliver it that way.
Replacing the pen after actually using it seems entirely reasonable - if nothing else, the needle will be contaminated.