If I could remember the quote right, I would refer to the beginning of a book by Milan Kundera. He claims that characters (in books in his case) do not necessarily depict real life people, rather do they reflect feelings or moments. Thus, one of his characters originated from "a rumbling in his stomach", and another from the german sentence "einmal ist keinmal", roughly translated "once is nothing".
That could be considered "rigid detail" to Milan Kundera, as these simple descriptions, to him, would describe a person's very essence. An artist or animator would probably not be able to extract the same depth of the characters.
So "rigid detail" is variable, depending on the team, the character, and the situation overall. In case of an adventure game character, I would say an entire page of text (hand--written) is minimum for a core character. Then again, we would all know exactly what I meant by a simple description like "eager youngster with a guybrush-ish wannabe-mad-scientist attitude". That
sure sparks an adventure-gamer's imagination, doesn't it?
All depends on the context I guess.