Your statements are correct, but I'm not sure I got the question. If you ask whether you may call async_read and async_write simultaneously on the same socket, then the answer is yes, of course.
The 'boost::asio::async_read(...)' and 'boost::asio::async_write(...)' functions might call async_read_some and async_write_some concurrently in some scenarios, as they do not synchronize accesses to the stream object that I'm passing to them as a reference. A look in their implementations confirms this: if the stream's async_read_some or async_write_some didn't satisfy the completion condition, it tries again, using the same reference to the stream object. With multiple threads calling io_service::run_one(), the result can be one thread calling async_read_some while another is calling async_write_some at the same time. This seems to prevent me from using async_read and async_write at all, so I'm wondering if the stream has some undocumented thread-safety guarantees, or if there's a proper way to achieve the same effect.