There is no contradiction, and it does not relate to working distance. But the Nikon manuals are somewhat confusing and it requires reading everything they have about it to get the picture. And, as with a few other features, it sometimes helps to read about it in user manuals for two or three different cameras. They sometimes give different details from one model to the next.
See the D7100 User Manual page 245 where it says the built-in flash can be used at either 1/320 or 1/250 when Auto FP is enabled. Compatible external flash units can use faster shutter speeds with Auto FP enabled.
If the shutter speed is above 1/250 and no higher than 1/320, with Auto FP enabled either the built-in flash or and compatible external flash can be used.
If Auto FP is not enabled, or if an non-compatible external flash is used, the shutter speed must be no higher than 1/250 second.
The key to what is happening is in the footnote that indicates "flash range drops as shutter speed increases" when shutter speed is higher than 1/250 and up to 1/320 with Auto HP enabled. What that means is that a flash unit that can work with Auto FP has a longer flash duration to allow use of a focal plane shutter that is not fully open during the entire exposure. Normally the flash duration is very short and requires the shutter to be fully open.
See also page 244 where register "e1: Flash Sync Speed" settings are explained.
The e1: register can be set for 1/320 sync speed. If the flash is used the shutter speed will be set to 1/320. In either Aperture Priority or Progam mode setting the shutter speed to faster than 1/320 will enable auto FP high-speed sync mode.
That is a little ambiguous about how it works with the built-in flash at shutter speed settings from 1/250 to 1/320. It appears that it is the proper setting for use with an external flash that can use Auto FP.
The e1: register can be set for 1/250 sync speed. The effect is as above except auto FP high-speed sync is activated above 1/250 shutter speed.
This appears to be a setting to use the built-in flash in Auto-FP mode with shutter speeds from above 1/250 up to 1/320.
The e1: register can be set to 1/250 to 1/60, and that will be the sync speed.
This appears to be the setting to get the shortest flash duration from the flash, by not using Auto FP mode. It would be correct for an external flash that does not have an Auto FP mode.
It is confusing. Worse than all of that... read the added notes on page 244 about "Fixing Shutter Speed at the Flash Sync Speed Limit". The note applies so using Manual or Shutter priority mode. I'm not sure what purpose this serves... :-)