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Hey, if he reported his presence on the bridge to an officer on 13th Feb, then he would not have yet known about the footage captured on Libby's phone. He was just covering his back should anyone have seen him around at that time, or if he was to be forensically linked to the area i.e. via a cigarette butt, spit, hairs, etc...
Edited to correct a typo/grammar
If this whole thing was meticulously planned as many suspect, then his actions in the hours and days after the bodies were found would have been a big part of his plans.
I think he knew the park warder, and made a point of bumping into him whenever he was on the trails, which I believe was regularly. Especially in the months leading up to the murders. Not for the purpose of finding victims per se. Finding a suitable location no doubt, but primarily more for gaining a trust alibi.
So when the bodies were discovered, he made a point of telling his family he was there. But he was always there. Hiking ? Hunting maybe? so they thought nothing much of it. He told them he would make this known straight away and headed off to tell his pal the warder.
And knowing the stand up Richard Allen well, the warder either forgot to tell anyone as it was unlikely to be this great guy he used to see on the trails all of the time or he told LE and they took his glowing reference as a good enough character witness.
Huge gamble by RA, especially when the video surfaced ( which definitely wasnt part of his plans!) But I guess he factored in how incompetent the authorities involved in this really were going to be.