I have nothing but sympathy for these people. I feel like I can relate to her, and I hope she returns to the US and applies for her visa so she can return to her life quickly.
As far as immigration rules go- How is an unassuming human being supposed to know when the people who run the country and it's services don't know??? This is exactly the trap I fell into. Before I came to the UK for my first extended visit I was 14 weeks pregnant and my intention was to meet my boyfriend's family and visit for 6 weeks before returning to have the baby in the US. While there, my boyfriend proposed to me (surprise!!) and he told me he had gone to CAB and gotten advice from them saying we could apply for a COA and get married in the UK and that I would have access to the NHS as a fiance. So the plan became to stay a little longer, get married in the UK with his family because the baby was still going to be born in the US with my family. Now the NHS staff told me all the same things, that I had every right to prenatal care and that I wouldn't be charged for it (nope- ate into all my savings to pay that bill off) In the end, I was able to find this forum, figure out my situation and we have been able to get where we need to be legally. I don't blame people for not being able to find out the answers when they go to people who should know, and get led astray.
Perhaps this woman should have looked into the legalities of her situation, but maybe her plan was to just visit, and then Bam! Pregnant.... so they look into getting married, the Bam! their precious daughter dies. I know I wouldn't want to bury my daughter and then leave my husband alone to deal with the grief. Of course lots of people have sad things happen to them and they had to suck it up and go home and do things the right way, it sounds like she's going to have to do the same- I just wanted to be one person to maybe understand where she might be coming from.... Things aren't so black and white, sometimes life happens and you can't plan for something you didn't know was going to happen.