TLDR: Scrubbing a mission does not unassign mission hardware and make it available for use on other missions.

Full explanation:
I had a pair of missions, a Manned Suborbital and an Orbital Satellite, planned for my turn. I checked the hardware requirements in the VAB: an Atlas + Mercury for the manned mission and an Atlas + Explorer for the Orbital Satellite. I had none of the hardware on hand. I autopurchased the Atlas + Explorer and assigned it to the Orbital Satellite.

Next, I visited the Launch Facility B and scrubbed the Orbital Satellite. Returning to the VAB, I tried to assign hardware to the Manned Suborbital. As I suspected, the Atlas rocket was not available. I checked the rocket count in Hardware Purchasing, which confirmed I did indeed have 1 Atlas rocket. Scrubbing the Orbital Satellite did not free up the assigned hardware, contrary to the popup alert.