Elsevier requires that authors do not do that - they can only provide copies of their papers in response to requests.
I also posted the PDF on my personal website immediately, on the theory that they are probably not going to sue me personally over my own paper. Not impossible, but I haven't gotten a C&D.
It would seem that the author personally received the email and replied with an attachment as a "professional courtesy", while completely automating the process in the background.
Are emails not considered communications "in writing"?
[paper-request] bacterial population analysis under exposure to fox news
?
And it would respond with the proper paper or papers attached.