Are you sure you're buying an Interrail pass and not a Eurail pass? I just checked and Hungary is in the list of residency countries:

Alternatively, just go to the station and buy one there.

That is not that easy in HU on MAV. Out of tradition from the old system in communist days INTern. tickets are only sold at a very few happy nr of stations-which as such is an improvement, as before they were only sold at special KASSA in town for that. If INtern. trains serve stations, sales are usually limited to only the stops that trains make. Is also due to different needed ticket/cashment systems-just ike it used to be in NL and BE. But the unit at Bp Keleti can always do it.

But I also think Gyula has simply clicked on Eu rail and not INTER.

In the autumn I bought seat tickets from https://jegy.mav.hu/ The service worked well, the Cheap tickets were sent by e-mail as usual.