I'm glad your friend has had her baby. However, I would just like to say a couple of things about the websites cited here. Firstly, who is behind 1to9months.com?? The disclaimer on their website says:
"The views expressed on this site unless explicitly mentioned are not necessarily those of the panel of Doctors."
Secondly, www.betterhealth.vic.gov.au - which gives the information about the placenta deteriorating at 38 weeks - may be produced in consultation with Royal Australian and New Zealand College of Obstetricians and Gynaecologists (and I'm not slighting their competence) - but it doesn't produce any hard facts. The line is couched in possibilities and vagaries: "38 weeks or so", "may not get enough oxygen". I don't think that these are good enough reasons to start shroud-waving about the need for induction. There may be a slight risk with waiting, but it is still a small risk. There's a much higher risk of miscarriage from CVS or amniocentesis testing. I could be cynical and say that those risks are deemed acceptable to alleviate the 'burden' to society of a handicapped child.
I'm not saying that perinatal death doesn't occur, or that monitoring of the foetus / placenta wouldn't be a good idea when post dates. However, I would rather look at serious analysis of the danger in properly documented research in a journal like the BMJ - where conclusions are accredited and can be statistically judged - than rely on someone's opinion from a website which isn't professionally based.
I believe there is an RCOG article called 'Nonsensus Consensus' which questions and undermines the blanket requirement for induction. Unfortunately you have to pay to get it. Might be worth it if you're in that position, however.