I previously asked a question regarding causative form of verb (Using もらう with に/を particle and passive/causative forms)
Looking at example sentence 5 (AさんはBさんに病院に送らせてもらう), this translates to "B let/made (someone/A) send (something else/ someone else) to hospital (as a favor for A)", or at least is what I wrote, and it seems from the answer that this translation is indeed correct.
Upon reading further on japanese causative forms, I stumbled upon https://www.wasabi-jpn.com/japanese-grammar/japanese-grammar-proper-particles-with-the-causative-form/ which states that the action taker is marked with the に particle (or sometimes を). Assuming that's the case, wouldn't the sentence translate to "A let B send (someone/A) to hospital"(normally used as first person), where the てもらう/てくれる only serves as a more explicit marker that A "let" instead of "made" B.
What went wrong with my understanding here. Any pointers would be appreciated.