高い does mean expensive without a doubt; not sure why you'd put a note about it ever meaning anything else when obviously in the context of "something valuable".
Just confused by that long paragraph, really.
I wouldn't normally have added it.
I more so remarked upon that it was strange that I felt compelled to note that “時計” can mean “clock” or “watch”, and that I felt compelled to note that it's the interpretation of the translator that it's a “watch” even though the context makes it quite clear, but that I somehow didn't feel compelled to make this note about “高かったネックレス”.
I think the reason might be that even absent any context whatsoever, “高かったネックレス” to taken to mean “expensive necklace” on it's own, whereas “時計”'s meaning here is interpreted by the translator. What probably also helps is that in the case of “高い”; it actually feels like two different meanings of the same word even inside of Japanese. But with “時計” it simply feels like one word, not two different meanings, it just so happening that another language, in this case English, has two words for that depending on the form factor. Much as in English “to wear” does not feel like three different words, even though in Japanese three different verbs exist depending on what one is wearing.