The Americans don't have to - in the end it was fudged with the USA that they used the same frequency - the yanks can just shut it down if they want to
Theoretically, they can now in effect transmit their own signal over the Galileo one, thus rendering it unusable while not affecting GPS.
Unfortunately, the resources don't exist to be able to do so for up to 30 fast moving targets in low Earth orbit - if it were that easy numerous countries would have done that to GPS long ago. It's simply far easier, not to mention cheaper, to fly an F15 with an ASAT and shoot them down. The Chinese have the same ability as well. That's not to mention the particle beam weapons that the US and British will have deployed within the next 4 years.
Trust me, if it ever kicks off big time and the US or China suspect an aggressor in using Galileo for military purposes, the entire constellation will simply cease to exist rather quickly. Not that the system now seems likely to ever be fully mission capable, and has little prospect of on going maintenance launches of new birds as the system ages. Great idea, but flawed, under funded, and liable to be destroyed or rendered permanently inoperable in the event of even a limited war.