Thank you for the careful analysis.

Of course, [one change implies two more changes]. In doing so, sentence becomes one of expressing gratitude for [...], as opposed to the generous act of referring clients who are receiving medical services from you.

Without the three changes, the sentence is (the original) "We thank you, for you're patients." I don't know how that could be "gratitude for referring clients" which might be expressed as "We thank you for your patients" (requiring two not zero of the three changes, though I think s/your/our/ would be an even closer match).

The original message is doubly polite for both overtly expressing gratitude and also for going almost to extremes in stretching normal usage in order to avoid more traditional and derogatory terms used to refer to the, um, non-employees of, for example, an asylum. (Not to mention acknowledging that more than one such person might have been impacted by the unfortunate mishap.) But not all, um, non-employees always appreciate such effort at courtesy.