Maybe not so formal as a presenting a fake ID but telling searchers or one of the first deputies on the scene "what they wanted to hear."
By your excellent timeline if BG slowed down at all, maybe sitting down from the emotions after killing, maybe he did not get going before 3:14, and then was presented with DG hustling up down the trail, calling out, probably flat out yelling, panicking, making phone calls and talking to anyone he met. This would box BG from going west on the north side.
Getting to his car after 3:14 would have taken time, to steal his way along the trail or go around on south side with exposure along I25.
Possibly his need for cover slowed him down enough that he crossed paths with the first incoming police at the trail head or near his parking place. They may have asked a some perfunctory questions and "he told them what they wanted to hear."
BG was seen at Freedom Bridge at 3.02 so that was before Derrick had even arrived or spoken to FSG. No police were there till after 5 when Mike spoke to his LE friend. BG was lucky and I certainly think he was gone from FB/CPS area by 3.15 at the very latest.
See timeline below
3:02
Possible suspect is seen at Freedom Bridge (not sure by whom?).
3:11
Derrick, Libby's dad call Libby while passing Wilson Bridge, no answer, he leave message at voicemail; he is almost there.
3:14
Derrick, Libby's dad call Libby again saying he has arrived at the meeting point,
no answer just voicemail, so he walk towards the trailhead, didn't see anybody.
Derrick walk further and meet an older man (the old FSM man witness?), coming from the high bridge, and ask him if he had seen the girls, but he had not but tell Derrick that there
was a couple (a man and a woman) under the bridge. Derrick then take the trial leading down to the creek to see if the couple was there, but Becky (Libby's grandmother), who is telling all this, does not remember if Derrick saw the couple or not.
Derrick then walk back to the meeting point.
3:30
Derrick call Becky telling her that Libby's not answering her phone and now the calls goes straight to voicemail.
3:30
Becky calls and sms Libby, but no answer.
3:35
Derrick walk down to the Freedom Bridge and on his way he meet the older man again (the FSM witness ?).
4:00
Derrick has walked back to the meeting point.
4:00
Becky calls her husband Mike Patty at his work and tell him she had called and sms'ed Libby, but no answer.
Becky tell Mike that they will go to the bridge and look for the girls.
Mike Patty says he will leave work at once and come to the Bridge and look for Libby and Abby.
4:??
Tara German (Libby's aunt) leave Becky's house 10minuts before Becky and when Tara
got to the meeting point she got into Derrick's car with Derrick.
4;??
As Becky leave her house Cody Patty (Mike Patty's son) come pulling in. He has just gotten out of work, Becky told him what was going on and Cody got in the car with Becky, and they headed to the meeting point.
When they arrived at the meeting point there was a lot of cars there also cars that did not belong to the family says Becky.
Becky call AT&T, bc Libby had reset her phone the week before, and Becky asked if they could ping Libby's phone but they said they could not do it.
4:18
Becky calls husband Mike Patty again
4-5:00
Mike Patty says that they, as a family, had searched the area, couldn't find anything.
5:15
Becky says "at this time Mike come walking up, he had been searching too" (at the meeting point) "when Mike got there he pulled in to Mr. Mirrore's driveway because there was no place to park due to so many cars".
Mike Patty call a friend who is a police officer.
5:15
Becky, after a long time talking to AT&T, give up talking to them because they could not help.
5:20
Mike Patty call the police
This is clear to me when reading this, that BG was gone before Derrick even arrived.