I think the main concern is for the police and social services at this point is the fact they've not made contact.
The media speculates, as it does, but there is some reason to be concerned that they've not even made contact with someone to say 'hey, we're all good, we just don't want a conventional life'. It's concerning for all 3 of them that they haven't done that. I believe that's why this has gone from a private affair that began in a bizarre way to a public affair where the general public are informed.
It is possible that the mum and the baby have in fact been checked out by a medical centre who, unless they have concerns about the infant, can't pass on those details to other services -- even the police.
Again, my social work training was a while ago and things change, but we have things similar to HIPPA here which means health information can't just be casually shared unless there's a concern for the health and welfare of the child.
So it is entirely possible mum and baby (and even dad) have gone to a walk-in health centre, since an A&E is possibly too public and may have police in by chance, been checked over, and the professionals who checked them have no concerns for the infant, or no concerns that raise the bar high enough to involve social services. (ETA: This is just IMO, there is no proof this has or has not happened.)
It is a very very tricky line to cross between people living how they want, and keeping kids (especially newborns) safe. It is one professionals on both sides have to consider when it comes to sharing information between services and especially with the general public and media.
Would I personally have concerns if I knew that mum and dad are sleeping rough with a newborn? Of course, but that would be coming from a personal, emotional angle. If someone is thinking with their professional head, they might not think their non-conventional life is concerning enough to elevate it and break confidentiality.
If medical professionals started giving information to social services every single time they had a personal concern that someone isn't raising a child the way they would, then people would stop going to medical professionals out of fear. It isn't always clear if there should be a concern. If a baby presents with frequently broken bones that it couldn't have broken by itself and has no medical condition that causes that fragility, then of course social services should be involved -- that's nice and clear. Obviously, this is me being extreme to make that point especially clear, that there's levels to concerns about a baby or child.
But someone going with a healthy baby (and you don't have to disclose how or where you're living) that you may think could be swaddled better or is a little chilly or has parents who don't live the same life you live makes it more complicated. You can't report an otherwise healthy baby to social services just because the parents use a box instead of a crib, for example. You may refer them on to parenting services and try to get them home visits, but they have the right to refuse those things, too -- again, without that raising the bar of concern high enough to ignore privacy.
My main point, mid-ramble, was that it's entirely possible they have had medical exams, but that the concern continues from the angles of social services and the police because these people have made a choice not to be in contact with them or someone who can verify that things are okay.
