Looks like you were right! The gravitational effects win out over the opposing effects due to the high speed of the satellite.
“the relativistic time slowing due to the speed of the satellite of about 1 part in 1010, the gravitational time dilation that makes a satellite run about 5 parts in 1010 faster than an Earth based clock”
http://en.wikipedia.org/wiki/Global_Positioning_System#Relativity
Actually I was using that example to show when I was wrong : ) I learned it the hard way when I was helping design the guidance system for the Tomahawk.