The sentence "János nem jól" doesn't have a verb, but "János nem jól van" is incorrect, because you can't use "nem van", we use "nincs" for that. See in detail and a bit better here: http://www.hungarianreference.com/Van-is-exists-omitting.aspx
Both true, but not quite why I was asking the question. I was thinking about how the to be verb "lenni" is typically only used in the third person when referring to location/existence or posession such as "fiam van" or "ott van az auto;" however sentences where description is involved like "Az az alma piros" omits the lenni verb. I see it in my magyar angol szotar, so I don't question the validity of it. The reference Bence shared is helpful. It's because jol is an adverb rather than an adjective.