I wouldn't say it's strict parenting, I would say it's possessive parenting.
The opposite would be;
they give their child to any passer by when her nappy is dirty, rather than actually do it themselves.
lots and lots of photos posted on fb, even naked ones, when their pages aren't secure.
no cuddles unless she's smiling - don't quite get that, tbh.
allways out on the town, leaving her with anyone who will babysit/the local 14 yo and her dodgy boy friend.
always getting someone else to push the pram, not really caring if people don't look both ways when crossing the road pushing her pram.
having loud parties in the house, which means she can't sleep.
I doubt any of their parenting style has been suggested by the HV, but apart from the no cuddles if she's not smiling, it all seems in her/their best interests, if not yours or you families.
As she grows older, they will relax (I hope). Keep offering to help out with her....they might really need you one day. It takes a village because parents are only human and will probably, at some point, be knackered.