Since I'm 100% certain I know where I am standing. I'm 100 % certain the GPS position calculation is correct.
If you have a GPS receiver you can verify that it does in fact report your location correctly.
I have designed and built GPS receivers, I have used a couple of different chipsets, and all the smarts are embedded in the chip sets these days. Most provide a simple interface, the standard is NMEA, but there are other interfaces, SIRF have their own, UBLOX are nice, you can get access to raw data. Apple iPhones don't even have the NMEA data in the API, some Android phones do.
But if you want verification of more than just what the NMEA sequences will tell you then you need to look at the raw data, the raw data contains the WGS-84 co-ordinates of each satellite that the receiver can see, and the distance to each satellite, each set defines a spherical surface, and with multiple intersecting spheres you can get the receiver location.
The transmitters can be anywhere, they don't actually need to be in orbit, all that is required is that the transmitters transmit their actual location, if they don't then the system will fail to report your location correctly.
When you look at the data stream you find that they are actually in orbit where they are supposed to be. (see the constellation positions I posted earlier, for some idea of what it looks like)
You can prove it all to yourself, you don't have to take my word for it. Just get a GPS receiver with raw binary data capability and write your own software to decode the raw data stream.
Here is an example of raw data.
Getting the pseudo range data requires a GPS receiver that will allow access to the raw binary data stream, and a bit of software.
34357445.85408 104694103.10708 25567381.586 9 25567371.842 9 25567379.669 7 76.000 84.000
Those numbers in bold, are the range to the satellite in meters, three readings, all around 25567380.000 meters, which is 25,567.383 km or about 16,000 miles away.