I don't recall seeing any posts from our VI confirming the time as around 2 PM. I saw one that said that LE had confirmed that RT was at that location at the time he said he was - but he told the family around noon, IIRC, and he told LE that he searched for an hour or so. I don't think we know for sure when those photos were taken. We only know that they exist.
There's definitely a chunk of time missing from the timeline, no matter how you slice it.
And yes, RT would have known that LE does not patrol the area, but rather responds when called. IMHO