This isn't about shooting down a rocket. This is about disrupting the launch complex. It's about sending enough energy into a complex that computers, the ones in the offices, stop working reliably enough to launch. It is possible, but imho would require a dish far to large to fit on an aircraft. So I agree that it doesn't exist, that this is propaganda.
EM interference is why launch complexes use fiber. You don't want a lighting strike near a 2km cable to cause a squib to fire somewhere. Lighting protections also protect against EM attack.