What an interesting thread!
I've messaged people on "Ancestry" a few times, hopefully, as Mart'n'Al suggests, clearly written, making names/dates/connections concisely, and explaining what I'd like to clarify, or "correct", and usually have had replies, even if the person cannot help / is not linked with the "one I want"/ does not wish to discuss it.
All - so far - have been courteous, if not all very elegantly written - does it matter as long as good communication takes place?
I've always replied to messages I get, either confirming a link, or accepting a correction, and seeking help, or guidance and explaining, or at times explaining why it isn't the same person they think it is.
From time to time I've had to explain, as Kiltpin did, exactly why person A in their tree is not person B in mine - and usually seem to have managed to get the message over, although not everyone bothers to "do their corrections" , probably because it'd lead to a lot more untangling of errors!
I really do like Andrew Tarr's lovely description of coming up with a theory and then seeking only the facts that support it - and here I fear many people are far too swift to act on "hints" as if they are "facts" without checking it all out, certainly not seeking out original sources.
But that will always happen. If they are happy with that, then there's nothing more that can be done.
The very few who then follow up an initial communication with what really amounted to "So, just do the entire job for me, unto the fifth generation, supply all dates, censuses, birth marriage and death dates and locations... because I can't really be bothered ...." will get a courteous reply suggesting where they can further their research.
(And the same happens on here, doesn't it, someone puts a query up, loads of people kindly use their own resources, getting heaps of information, putting it on here, and then there's the wait for the person who put the original query up to confirm, or thank the people who have magically done weeks of work almost overnight - that is, if they get back in touch.)