Not in anywhere near the same manner that someone is affected by being forced to stay in an unhappy marriage, no. Parents worry about their kids - that's normal - but your kid being transgender doesn't (or at least shouldn't) fundamentally alter your relationship with them. They're still your kid.
So you don't think finding out "your son actually identifies as a girl", and finding out that their 7th grade teacher knew that before you, and you found that out via reading a different name at the top of your child's homework isn't seriously "life disrupting" or jarring, even more so than a divorce?
The primary reason for this is the potential for abuse. There's a difference between saying "hold on, let's not rush into this" and completely rejecting or dismissing your child's feelings. There's definitely room to train school staff to recognize those differences when a student comes to them (because some kids may interpret "lets not rush into this" as a rejection), but I can understand why schools might want to err on the side of caution.
Broadly speaking, the law does allow teenagers some degree of bodily autonomy, so I don't see it as strange that parents would not need to be identified if their child was experimenting with a different gender identity. Many states allow girls to access birth control without parental permission, for example.
Per the story in the NY Times article, it sounds like the parents were supportive, but they were really upset that they weren't kept in the loop.
With regards to childrens' feelings...not giving them everything they want shouldn't be considered synonymous with "ignoring their feelings". Had that been true, then all those times I told my parents "you hate me!" (because they wouldn't let me to go parties at other kids houses when their parents were out of town) would've been valid, obviously they were not. They simply didn't want me smoking weed and drinking at some random person's house absent of any and all adult supervision.
Children (especially during adolescence) are prone to over-reaction, emotional response, impulsiveness, and "act first, think later" mentality.
There's a reason why we don't let 15 year olds drink, drive, vote, get tattoos, own a gun, join the military, get married, etc...
(and those are all less impactful and more reversable than a gender transition)
The premise that "they're absolutely sure, and they know for sure what they want" at that age is a questionable assertion, and people are right to be skeptical. That's not to say that some trans people and non-hetero people didn't know exactly who they were and exactly how they felt and that carried into adulthood...obviously you can find cases like that.
But people in the 13-17 age range are prone to fads or what they think will make them rebellious or cool. The statistics would suggest that in present time, a 14 year old claiming to be trans is just as likely to grow out of it as a kid who want to be an astronaut when they grow up.
Better analogy, though - for the most part - teenagers are not undergoing surgical gender confirmation procedures (especially without parental permission).
it doesn't have to be full blown surgical in order to ruffle some feathers. The parents in the NY Times article sounded pretty progressive, but also were still a little put off about being kept in the dark about what was going on with their kid.