As per happypuppy's comment on iterinfinitas' sentence, shouldn't 「~必要はない」 also be included in this section? It has the same meaning as the uses outlined above.
Yea - means the same thing. I don't think I have a grammar page up for that yet, so I'll add one when I get a chance. A lot of the grammar still (unfortunately) isn't sufficiently linked with similar/same expressions, but it'll happen! I need to make a tool to let users suggest links so the burden isn't completely on me.
It wouldn't fit in that well with the way the grammar dictionary is organized on the server. I'll think about if there's a better way to handle it, but for now, the best is to have a separate page that links back to this.
The second example sentence looks to me to have a completely different meaning than the other two and the explanation. Take a look: 「手で渡すことはないので、手紙で送って下さい。」 It's not something you can pass by hand, so please send it in a letter.
This example is defining what type of thing (こと) we're talking about, specifying that it's a thing that's unable to be passed by hand. We're restricting it, not saying it's okay to not do it.
So, if we're talking about "A is not necessary; it's OK if A is not done." or 必要はない things, this example belongs under a different heading, or perhaps over in the こと entry...
That said, it clicks well with the Japanese grammar in the (very shallow) depths of my brainpan. I understand the sentence perfectly well, even though it looks contrary to the other two examples and the English definition of the grammar point.
The first example sentence 「いいえ、誤ることはないよ。」 - I thought that 誤る (あやまる)means to make a mistake or to err or to mislead, whereas 謝る (あやまる) means to apologise. Can 誤る (あやまる) also mean apologise or should it be the other kanji?
Is that a user sentence? If so, you can add a comment directly on it.
It's an example sentence for this grammar item, I think it was even the quiz question I got. I found it in the dictionary, and from there I could copy a clean version (copying from the quiz added the extra spaces): 店長も先ぱいもいないのに、真面目にやることないよ