I frankly don't see why that would be my parent's decision; after all, I'm not under her legal authority. And having an Alliance admiral be involved with the process at all would get too messy, with too much chance of information leaking.
Of course, my Shepard does not have to worry about any of this, because both of her parents were horribly murdered.
Whether or not you're under legal authority, a parent is the next of kin if the person is unmarried. Legally, unless specified in a living will or DNR, the next of kin has medical rights. Which, doesn't apply in fiction, but nonetheless.
I think it's pretty telling that you cannot even for one moment, see any other side to the argument than your own. Which is why I think you're a little biased on the situation. As I said, I can certainly understand if Liara is your significant other, but it's a bit "broken window" not to acknowledge that for someone who really didn't give a flip about Liara, would be perfectly fine with having her decide anything of that priority.
I can't speak for my own parents and I certainly wouldn't speak for anyone else's, but I don't think you'd find too many who would disagree that if there was a major medical decision to be made that would affect their child's entire life--adult or otherwise--and a casual friend stepped in and not only over-ruled them, but didn't even consult them before making the decision for them....it would be some bloodshed going on. It would be completely unacceptable. After seeing Dr. Frankenstein's portfolio, I wouldn't take my dead kid to him and be like, "Hey, I know that last one didn't work out so well, give this one a shot!" So, I absolutely wouldn't want someone else to do it.
I understand if it's a lover. I mean, you discussed the future, you're invested in their lives. Their future is your future, so on and so on. But a friend? A casual friend? I mean, I love my co-worker. I would do anything for him. Maybe even donate an organ to save him. If he died, wouldn't drive him over to Pet Cemetery and think, "Well, don't know if he is coming out good or bad, but let's chuck him in anyway! Least he'll be alive!"