I do not disagree.

I feel pretty certain that she had possession of his phone from Sunday on.
I am more interested in learning
when the internet search took place. Was it Sunday night? Was it during the 4 hours? Was it when she returned home (without him)? I, personally, feel this internet search is going to prove pre-meditation on her part. Among many other things!
It will also show the level of planning she went to to explain things away. For example; the search was used to report him as a runaway. However, it was
really a cover-up (on his part?), to hide the fact someone was sent to pick him up. Despite the fact LE never considered him to have been abducted, T wanted to plant seeds of doubt, and cast suspicion elsewhere.
Then there is the fact that she left her phone at home, but took Gannon's phone with them. Why is that? If she were concerned Gannon was going to run away and take his phone with him, why would she give him the opportunity to do so? She obviously did not take into consideration he could have been tracked and found by now?
For me, Gannon's phone and the internet search she claims he made play a large role in the investigation. It put this whole case in motion. It's the first lie revealed. It was what she thought would protect her from suspicion. It's exactly what she tried using to blame Gannon's disappearance on Gannon. I don't like her. At all.