That rule is mostly true, especially for simple verbs, but it's not always true. There are a few exceptional cases where what was originally a transitive verb is now interpreted as an intransitive verb.
One example is 暮らす, which is normally regarded as an intransitive verb today. According to 明鏡国語辞典, it was originally a transitive (or causative) version of 暮れる, but something like "to make days end" eventually became an independent intransitive verb meaning "to live (a life)".
When it comes to compound verbs, there are quite a few intransitive verbs that end with す, including 踊り明かす, 泣きはらす, 鉢合わす and 怒り散らす.
As for 出くわす, I could not find any authoritative source regarding its etymology. But it may be related to 交はす【くわす】, which is a transitive verb meaning "to cross/exchange (something)" in classical Japanese (its modern equivalent is 交わす【かわす】). This may be another example of a verb that changed its transitivity while being used as a compound verb. Cure Dolly's rule is useful when you learn words, but this is not a rule recognized by an average Japanese person, and there is seldom a 100% correct rule in the world of vocabulary, anyway.