A friend was writing a technothriller screenplay and I did extensive research on nuclear weapons manufacture for him. I told him I hoped he appreciated how much I was adding to my file for his sake. I was half-kidding.
I dunno. I get that this sort of thing is useful in court, but people are naturally curious about a lot of things. It doesn't always mean they're actually planning to do it all...
That is, if they had just picked up the joining of everyone that had searched for the details of child death in a car with those that had had a child death, that would be different. In this case, they had suspicions already, and are stitching together details from computer history as well as cell records and such.
This is all to say, when potential crimes happen, I personally think investigating them is not a terrible thing. Instant vilification is, but that is a different topic all together. Same for basically fishing for reasons of suspicion.
Now, if this was something much more abstract such as three of the past unknown books they have read in the past unknown years involved accidents of this type, that would be one thing. But this? Doesn't seem that far fetched.
Edit: to clarify further. They had probable cause already. The suspect was acting ridiculously suspicious. The web browser behavior is just additional data, not the sole data.