Riven, sadly some Americans do believe this. I left an American parenting forum several years ago because I naively wandered into a debate about healthcare insurance and made the mistake of simply describing:
all the medical treatment I had received or had access to during pregnancy and after giving birth (scans, blood tests, parenting classes, midwife and consultant checks, 7 days in hospital because DS had jaundice and wouldn't BF, breastfeeding counsellors;
follow up support (midwife check-up for 10 days after birth, immediate access for DS to paediatrician at hospital for 2 months after birth, weekly baby clinic, BF support group at hospital, mum and baby group, PND support);
free prescriptions and dental treatment during pregnancy and for 1st year after birth. Free prescriptions for DS until age 16.
(I'm sure I've missed loads of things off the list here, but you get the gist.)
I them that this was all free in the UK. The American forum members were mostly surprised and shocked and a sizeable minority just refused to believe me. I was accused of having a political agenda for joining the forum. "European Commie propaganda" was one of the politer terms used.
Fortunately other UK members confirmed everything I'd written. It all caused a lot of bad feeling and I stopped posting there.