“The distance quoted is likely the range as compared to a Minuteman’s 6,000 miles. “
While the exact range is still classified, I can assure you the MMIII goes a LOT farther than 6,000 miles.
http://www.af.mil/About-Us/Fact-Sheets/Display/Article/104466/lgm-30g-minuteman-iii/
BTW I was a Minuteman III Missile Systems Analyst (AFSC 316X0H) in the USAF for 9 years. We put many in the lagoon at Kwajalein from Vandenberg AFB and that range agrees with your statement.