it looks like I parsed it wrong
You parsed it correctly. 人多嘴雜 is not a non-compositional "
idiom". Its meaning is actually the sum of the meanings of its components (i.e., the meaning of the form /AB/ = the meaning of /A/ ⊕ the meaning of /B/, with “⊕” denoting ‘combined in accordance with the rules of the language’; e.g., 人多嘴雜 = 人多 + 嘴雜: (1) 人多就會嘴雜, (2) 人多因而嘴雜, or (3) 人多而且嘴雜, wherein “⊕” denotes '就會/因而/而且').
嘴雜 involves a metonymy--a figure of speech in which 嘴 is substituted for 話 ('talk, remarks'). 雜 may be literal (meaning '紛紛, 多種多樣") and thus 嘴雜 may refer to all sorts of talk or remarks, especially scandalous talk or negative remarks as in "醫院人多嘴雜, 你來這兒, 不怕別人說是非嗎?". It may also be figurative (meaning '交傳, 傳來傳去') and thus 嘴雜 may refer to the spreading of gossip, as in "醫院人多嘴雜, 你來這兒, 不怕被人張揚出去?"
To me, it is not unidiomatic to treat 嘴雜 as a phraseological unit, for instance:
風傳媒 2020-06-18: "國民黨的組織像流水席餐會, 人多、龐大、
嘴雜、老化..."
之乎: "小单位
嘴杂怎么办?"
蒙克顿枫下论坛: "缸浅动静大,
嘴杂是非多."
狩獵美人心: "
嘴雜, 就會產生許多的八卦."
医院人多嘴杂...Is 嘴杂 an adjective or verb
醫院(topic)人(subject)多(predicate)嘴(subject)雜(predicate)
人多嘴雜 is composed of two clauses (i.e., 人(subject)多(predicate) + 嘴(subject)雜(predicate)) that together form an adjectival predicate for the topic 醫院.
國民黨的組織像流水席餐會, 人多 (adjectival)、龐大 (adjective)、嘴雜 (adjectival)、老化 (adjective)..."
小单位嘴杂(adjectival)怎么办