Is it part of your PTO's mission to fund Eagle Scout projects? If not, then there's your answer. Your tax exempt status revolves around your doing things that fit in with your mission. When you report your income to the IRS, you have to show how it ties into your mission. It's the same reason that you don't run "Pennies for Patients" or "Jump Rope for Heart" money through the PTO's bank--it's not in your mission to fund cancer or heart research.
I don't know enough about how Boy Scout troops are set up, but seems like they should be able to run the money through the Boy Scout troop and get a deduction for it that way.
If the project being done by the Boy Scout is something for the school that you might be willing to get behind--like a gaga ball pit being built for the playground, as an example--there might be a way to structure it so that it is a PTO project for which you are soliciting funding, but the Boy Scout is doing the work as a volunteer for the PTO. But that's the only way I can think of that would make this legit.
The VP at our school is asking PTO to extend their 501c3 and take in donations for an Eagle Scout project so the businesses can get a tax deduction. I am looking for info on why this isn't allowed because it just doesn't sit right with me. Please let me know!