What makes you think that? KB has definitely been in the news in both places, and I would assume that LE in both places are on alert for relevant evidence, if not actually proactively searching for same.
My current theory is that KB and baby K arrived home from Safeway to find him waiting or just arriving -- or maybe they connected at the store and he followed them home so she could drop off her car. Then they headed out either to get a tree, or for Thanksgiving dinner at his place (and she brought her groceries with her, including the ingredients for whatever she had asked her mom about earlier).
She hadn't "done" her hair, per CB, but if they were going to get a tree first maybe no need. She might have hair and makeup items kept at his house to get ready for dinner.
Then something went wrong. Maybe while getting the tree. Maybe even after dinner, but that would require PF's mom to lie about it, denying KB had been there (presumably) so I'll guess maybe it happened before their holiday dinner, and he simply told his mom KB wasn't coming for dinner after all.
Of course it's also possible they actually did break up and KB actually did plan a getaway for a few days while the baby stayed with PF, but then something happened and she never made it back home to get her vehicle and pack for her trip. I don't think that's likely though, but I know reality often is complex and more than one story can be playing out at a time.