This one is tricky, because I can kinda empathise with your friend's position. I was very attracted to the idea of freebirth when I was pregnant with my first, because I am someone who tends to be very self-reliant in life and whose experience has taught her that depending on other people is often disastrous. Indeed, that mindset gave me an acute fear of flying for nearly a decade. I had fairly significant issues with trust and unfamiliar individuals, however much I knew they were skilled and experienced in a discipline.
Of course, my pregnancy soon challenged all those fears I had, and made me realise that, sometimes, it is impossible not to depend on an unknown and unfamiliar third party.
But one thing you never read in these threads about childbirth and choice is that it is common to be in a position during labour where the experience, in the moment, renders you, as the birthing mother, unable to respond and react in a calm and logical way to your circumstances.
Unless you've experienced labour yourself, it's quite difficult to imagine how the combination of tiredness, intense pain and extraordinary biochemical and muscular processes can leave you so unable to think coherently. I, for example, never thought I would become so fatalistic at 8cm dilated. 
I think a lot of freebirth advocates either don't realise this or forget this; there's very much this idea of "controlling" the situation. In truth, you are never so out of control of a situation in your life as when you are in labour. You can't stop the process and have a break to calmly think about what to do next. You might know something isn't right, but when you've contraction crashing into contraction, you can't really do anything much about it because you aren't in the situation where you can even think about it clearly.
So someone else has to be there to make those calls for you in your best interest, and you need someone who has some sort of experience so they don't pursue useless and ineffectual solutions.
But your friend, as it is her first, won't necessarily realise all this. She doesn't yet know how her body handles birth, let alone what her birthing personality is.
Personally, I'd let the realisation quietly dawn on them both. If it doesn't, there's probably nothing you could say to change their minds anyway. Sometimes, you just can't save people from themselves.