Hello there,
Yes, the explanation you talked about is an oversimplification, as with almost every "rule" for collocation.
The vehicle is too high off the ground. Getting in it isn't super easy because you kind of have to climb. (here, "high" would be okay, but in my opinion we would clarify with "off the ground"). "Tall" would be talking about the top of the car, the clearance: will the roof hit the top of the tunnel? How tall is the car?
Take the kid off the table! The table is high/tall and he could get injured if he falls off it. (both work; although "tall" is better, both might be said by a native speaker).
Thanks to the width and height screen of the TV, you can enjoy your TV without having to sit close to the screen. ("wide and tall" would be OK, but sounds unnatural. Even talking about the width and height feels unnatural in the first place; just saying "the dimensions" would be enough).
A bus is usually twelve feet tall. (See above)
Her desk at work is too tall/high for her. (both are fine; "tall" is probably if we think of the desk as a whole, and "high" is probably meaning the desktop, the surface on the top).
The table is 3 feet tall/high. (see above)
Since native speakers don't adhere to the rules, as you said, a contextualized approach, learning via input from books, podcasts, TV and movies is by far the best. Of course, sometimes you would need to listen/read analytically, focusing on one topic (e.g. your question today) and pick the appropriate resource (for today's question, perhaps a documentary on architecture, or a book on travel which describes places; something like that). In lessons with me, I use pictures to teach this sort of thing, a conversation, visually-focused, contextual approach. Words have almost no meaning without context; the more context, the more specific your understanding gets.