StoneyB's answer to the similar question linked to by your second here. Is all you need to read. However, I'll give you some other English usage information about the sentences in your question as well.
Answer: Yes, it's true.
A This sentence is fine but verbose. [Compared with and compared to are for all intents and purposes interchangeable here.]
B This road is much busier than ours. [This is idiomatic. It has one less word. Compared with is unnecessary because the content implies a comparison, so there's no need to say it. It's like Arnold Schwarzenegger saying something like Hi, my name is Arnold. I'm a man. You can tell from looking at him that he's a man.]
C The meaning of this sentence would be clear enough to most speakers, but it's not optimal. "Children seem to be learning more interesting things compared with when we were in school" seems better to me.
D This one isn't optimal either. "Children seem to be learning more interesting things than we did when we were in school" seems better to me.
The rule of thumb when making this kind of comparative statement is to use the shortest sentence possible to express the comparison. In most technical articles and articles in journals that publish academic prose, you'll see the longest possible sentences in addition to "as compared to/with" rather than than.