[derobert]

Two things:

First, GPS satellites are in orbit ~20,000 km altitude, so this rocket is nowhere near too high. The beamwidth is pretty wide (it covers the entire half of the Earth, after all). Some quick research shows that below 3–4000km, there isn't much difference. http://emergentspace.com/gps_pubs/SSVP-v1.07-2column.pdf.

You should be able to get exact orbits (to the centimeter!) from the NGS (http://www.ngs.noaa.gov/orbits/), if you're interested.

Second, its the receiver that sees the GPS satellites, not the other way around. The satellites transmit, the receiver does not.