DeputyUICHousto wroteIsn't the runner permitted to run the bases as long as it is done so properly?
The key word is properly. Is the base runner legally allowed to run through home and contact a defensive player making a play on another runner? No. Therefore no matter if it is an inch, a foot, or 10 feet, once the runner has scored and then makes contact, she has interfered, and this is interference by a retired runner, thus the run scores, the runner closest to home is declared out due to the interference by a retired runner.
Is this a fair ruling? Most likely not, but the rules don't specifically allow a runner coming home to run through the base, but they do seem to prohibit the runner from coming home and then interfering with a fielder making a play on another runner.
Here is something else to consider. How is home plate different than second or third. If a runner ran through second or third and contacted a fielder making a play on another runner, after having been retired, we have interference by a retired runner. The same principal applies to the play at home plate.