The Lewis Daynes' who didn't live in the place the Mum passed on wouldn't have to be checked out cdtay, because they weren't the ones the police were looking for (aside from the fact that he could have been lying about where he lived of course). Although it would have been cleared up pretty quickly if they had looked as they wouldn't be looking on LinkedIn they'd have been using their own databases, so easy to rule out who it was/wasn't.
The 'Lewis says' stuff you see on here is 99% about people the parents/DC know in RL (or who are in the immediate area anyway), so not really comparable to an internet random from possibly anywhere in the world/any age, and someone they can't get direct contact with easily.
A CV is hardly of the same importance as an underage child, and employers are quite within their rights to check out what's written on them, even to the extent of checking with the police for certain jobs (I think?).
Checking out reports of what someone's been up to on the net/comp/phone isn't as simple as just looking their name up (as far as I know).
For starters the person is most likely lying about who they are/where they are, meaning the police would have to find their IP address, then look at both ends of the conversations ie comps/phones (which has to be done properly if they're looking at gathering evidence), and that's just if they're in this country! If they're abroad our police don't have any authority and if it's someone up to no good they can re-route what they're doing all over the place so you can't pin them down.