As much as most people don't want to hear this, but almost all of those facts are correct, yes. (plus some more that aren't even listed there)
And i can tell from my own experience.
About your question what or when it is "too" low, now that differs with age and also gender.
Females need to keep a higher percentage than men before the first issues become apparent.
Men can go a bit lower before the troubles begin. (of course varying a bit from individual to individual as well)
Here are some general numbers:
1) Model ACE (American Council of Exercise)
Description-------Women------Men
Essential Fat------10-13%----3-5% (*essential being the absolute minimum before it turns into organ failure/fatal)
Athletes-----------14-20%----6-13%
Fitness------------21-24%----14-17%
Average----------25-31%----18-24%
Obese------------32% + -----25% +
2) Model Jackson Pollock
In this model it's taken into account that with increasing age, also your skinfolds change which normally are used to calculate the bodyfat levels. And a general need for higher bodyfat percentage as you age as well, in order to stay healthy. It does not take into account that older athletes could still have a strong toned skin and be generally more dense, so that's a float value you have to figure for your self when checking.
I can only speak for myself and for people i know whom i have whitnessed running into issues with low bodyfat levels.
For me - as a female - when i get close to or lower than 15 % all sort of hormonal issues begin (period begings to come irregular and too often or not at all), skin dries out, you can feel inflamation and lesser abilities to recover from workouts etc. (they didn't even list that on the page you had been on, but that's a commonly known issue as well - especially for the female gender, same as you guys get issues with your libido, sperm production etc when going too low.)
And you can get away with more horrible things - done to your body - the younger you are, but the more you get beyond 25-something, the more you should really think stuff over, and consider what you put yourself through.
So facit - yes. It is correct.
And that is also why you should think twice if you even "need" to get that low.
If you are a professional athlete or competeing, yes. Because when you do this as your profession, you normally should completely be aware of the health risks you put yourself through. Including injury potential and health problems. Every professional athlete should be informed and normally is completely willing to take those risks to reach their goals.
If you just want to be fit, and look good.. you don't need to get shredded to a point where it influences your life in a bad way. And you might just look better with a tad more fat too. (Hence facial fat get's always lost first - which tends to make you look slighty sick and somewhat unhealthy)