Hi there, they actually can charge you tax on that income. The tax laws state that PA can charge tax on any person who earns income in the state whether they are a resident or not. The states look at it like you couldn't have earned that income unless you used our state to earn it, so they should be able to tax it. Sorry it is not what you were hoping for, but they are correct. You will file a non-resident PA return.
If you have any follow up questions please ask.