Push and Fetch access are different.
RR does not support Push access, which is not supported with a POP account with a cell phone's mail client that communicates direct with the incoming mail server for the account as the iPhone's mail client does.
The only accounts that support Push access is a Yahoo account when created with the iPhone's mail client using the Yahoo account preset, a MobileMe account, and an Exchange account accessed via ActiveSync with the iPhone's mail client. All other email accounts are accessed via Fetch, automatically or manually.
Most ISPs block the use of an SMTP server that is outside of their network or not provided by the ISP unless the SMTP server is authenticated. AT&T is no different in this regard - you are using AT&T'a cellular network as your ISP when connected to their cellular network, and a RR account does not have an authenticated SMTP server. If Time Warner provided an authenticated SMTP server, you would be able to send with the account regardless the ISP used for your Internet connection, unless an ISP blocks the use of all SMTP servers that are outside of their network regardless if an SMTP server is authenticated, which is not common.
As already provided, you can use AT&T's SMTP server to send messages with the account when connected to the Internet via AT&T's cellular network.
Or quit using your RR account which has this limitation because Time Warner chooses to not provide an authenticated SMTP server. Gmail includes an authenticated SMTP server, can be accessed as a POP or IMAP account with any email client, and is free.
My primary account is my MobileMe account and I access a business POP account with the iPhone's mail client. Both accounts have an authenticated SMTP server and I've never had a problem sending with either account regardless my Internet connection or ISP being used.