I believe that the number of satellites refers to the precision of the measurement. Unfortunately, getting time precisely is very tricky. It is really an estimation process and the more satellites you have available the better the odds of getting a good estimate. Even the relative positions of the satellites changes the "dilution of precision" of the measurement.
There are all kinds of delays that need to be accounted for and they change unpredictably. It is more than the distance between the receiver and GPS satellite. The ionosphere is the largest issue. Then there are tropospheric delays. Also, the precise positions of the GPS satellites needs to be known and corrected for. That is the satellite's ephemeris data and that gets changed due to fluctuations in the gravity field of the earth (gravity is not constant everywhere on the earth's geoid) and the moon and sun play a roll. Multipath errors are signals that are reflected off of building and can spoof the receiver into producing a wrong estimation of the GPS time. Then there is clock error for the GPS satellite itself. Oh, I forgot about relativistic effects! Yes, orbiting space vehicles do have time dilation issues and the satellite's clock is pre-adjusted for it. There is also velocity of the space vehicle that changes the phase timing of the signal like a train's whistle as it approaches and passes you.
Using more satellites allows for better error correction for the above problems. There are geosynchronous satellites that measure the ionosphere phase delay (WAAS) and provide correction data for the various locations in the US. Europe and Japan have their own systems. All fall under something know as SBAS (Satellite Based Augmentation Systems). Tropospheric delays are estimated based on altitude, latitude, and longitude of the receiver and the weather.
Where the receiver is on the earth and where the GPS constellation is at any given time is another issue. Generally, you are guaranteed to get at least 4 satellites in view and 7 to 12 are more typical.
It really depends on the precision the end user needs. Power companies probably need to be much better than the millisecond. GPS should be able to resolve time accuracy to within 50 nS. However, as I pointed out, GPS performance is dynamic and constantly changing.