POTENTIAL GND CONFLICT WHEN 2 ACFT; A C525 AND A TURBOPROP; TAKE POS AT OPPOSITE ENDS OF THE SAME RWY FOR TKOF AT HXD; SC.

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HXD HAS 1 RWY: RWY 3/21. WITH CALM WINDS; WE ELECTED TO DEPART RWY 3 BECAUSE THE APCH END WAS CLOSER TO THE RAMP AND OUR DEP WAS NEBOUND. WE SAW NO OTHER TFC NOR HEARD ANY ON UNICOM. WHILE TAXIING OUT; WE BOTH SAW A TURBOPROP BEING TOWED NEAR THE DEP END OF RWY 3. MY COPLT MADE A BLIND XMISSION OF OUR INTENTIONS ON UNICOM. THEN WE TAXIED ONTO RWY 3 AND HELD OUR POS FOR THE FINAL ACFT CHK. AT THIS POINT WE OBSERVED THE TURBOPROP TAXIING UNDER ITS OWN PWR AND TURNING ONTO POS FOR A RWY 21 DEP. HIS LNDG LIGHTS WERE ON AS WERE OURS. WE BOTH REALIZED THE TOW VEHICLE HAD BEEN A MIRAGE (A WARM; SUNNY DAY). BY NOW; THE TURBOPROP WAS EXITING THE RWY. WHEN IT WAS BACK ONTO THE TXWY WE CALLED UNICOM AGAIN AND DEPARTED RWY 3. AFTER LEAVING THE TFC PATTERN WE CAUGHT ANOTHER MISTAKE -- OUR TRIP SHEET WAS MISREAD AND THE WRONG UNICOM FREQ WAS SET IN THE RADIO. THE LESSONS FROM THIS OF CHKING ONESELF; COMMUNICATING; AND CONSTANT VIGILANCE IN THE COCKPIT ARE OBVIOUS. NO MATTER THE EXPERIENCE; PLTS ARE ONLY AS GOOD AS THEIR LAST FLT THE NEXT ONE COMES WITH NO GUARANTEES. THE OCCURRENCE WILL BE DISCUSSED AT OUR NEXT QUARTERLY PLTS MEETING BEFORE YOU READ THIS. SUPPLEMENTAL INFO FROM ACN 544412: BE AWARE THAT HEAT RISING FROM A RWY CAN CAUSE AN AMAZING ILLUSION WHAT YOU THINK YOU SEE MAY BE TOTALLY WRONG. IN RETROSPECT; THE ODDS A COMPUTER ACFT WAS 'UNDER TOW' AT THAT LOCATION ARE CLOSE TO ZERO.