Does it mean "Hino-san's idiot" (indicating possession) or "Hino-san is an idiot"?
If it's the latter, why shouldn't it be "Hino-san は baka"?
Does it mean "Hino-san's idiot" (indicating possession) or "Hino-san is an idiot"?
If it's the latter, why shouldn't it be "Hino-san は baka"?
Possession is just one of the many meanings of の, and does not apply in this case.「ひのさんのバカ」 here means ひのさんがバカ, i.e. "Hino is an idiot" (as you suspected).
See: How does the の work in 「日本人の知らない日本語」?
While this substitution mostly applies to relative clauses or double-subject constructions (unless there is a direct object marked with を), the subject particle が can be replaced with の in many cases.
Refer also to the Jisho definition for の
1. indicates possessive (...)
2. nominalizes verbs and adjectives (...)
3. substitutes for "ga" in subordinate phrases. (See also が): 100人近くの人がいたが、ほとんど会ったことのない人たちだった。There were almost 100 people, few of whom I had seen before. (...)
The の is appositive (同格). The Wiktionary entry for の may help:
の
助詞
格助詞
5. 上の語と下の語が同格であることを表す。
- 部長の山田さん。
- 妹の薫さんが来てたよ。 (...)
- 悪態をつくときに用いられる表現。
- お兄ちゃんのバカ。
- 部長のわからず屋が。
The appositive の has been explained multiple times in this site:
Common/familiar examples:
『羊のショーン』 Shaun the Sheep
『おさるのジョージ』
『セロ弾きのゴーシュ』 Gauche the Cellist
「妹のメイです。」
「魔女のキキです。こっちは黒猫のジジ。」
The Wiktionary page says one of the usages of the appositive の is 悪態をつくときに用いられる.
This has also been asked in this site:
Common examples:
「メイのばか!もう知らない!」「お姉ちゃんのバカー!」
「ばあばのケチ。もうやめなよ。」
「クララの弱虫!」
「ペーターの意地悪。」
「おばさんの嘘つき!」
There are various opinions, but my conclusion is "this construction is hard to explain perfectly based on simpler grammar rules". I can say the following sentences are all valid:
の in Sentence 3 is clearly not a substitution of the subject marker が/は; the subject of this sentence is undoubtedly 太郎のバカ as a whole. However, の in Sentence 2 doesn't seem to be an apposition marker to me. Unlike バカ ("idiot") which is a noun that can represent a person, エッチ is a na-adjective and cannot represent a person. We can say バカが3人いる but not エッチが3人いる.
Therefore, I think it's best to regard this as a special construction that can be used only in the context of abusing someone, like English "You idiot!". "太郎の天才!" is understandable but sounds like a joke to me.