I am not always impressed with the knowledge of ISP support people, and Mail, although it is good to hear yours has some Macs. I am pasting in some general comments, I often offer, to explain all the questions I ask about server authentication -- it may help clarify why a person may need to first have and authenticate an incoming account with their ISP their SMTP.
There are even some ISP who provide two different SMTPs -- one for use when at your home venue, and another when traveling. The one for use at home is not authenticated by password, but by the IP address of the modem, and it is further pointed out that the second one (authenticated by password) will NOT work when at home -- this is platform and mail client universal, and not limited to Macs and Mail. The one with Password Authentication is needed when on other networks, such as in hotels and cafes. But not all practicing this form of home system authentication are so explicit in their description.
When authentication of the SMTP is what is called POP3 before SMTP (or SMTP after POP3), no user name is appended to the name of the SMTP, and some providers will explicitly direct that SMTP authentication be set to None, but others may be less explicit, depending instead on samples of setting up an account in a common mail client such as Outlook Express. There are not exact parallels in the dialogues for this between Outlook Express and Mail, but it can be interpreted, with care. In the SMTP after POP3 type of authentication, the redundant step of separate authentication of the SMTP apparently times out and fails, rather than explicitly being refused access.
When the name of the incoming and outgoing servers seem the same, it can often be that SMTP after POP3 authentication is being used, but not always.
This can also result with cable broadband providers, who can authenticate you for sending, based upon the IP address in the modem they provided you.
When an ISP provides no separately authenticated SMTP, there may be no way to send mail when at a hotel, cafe or other hotspots. This is one of the advantages of having a .Mac account (or also a Gmail account), and the use of an authenticated SMTP. Of course certain providers of home networks block this and other third party SMTP on Port 25, and thus the often seen discussions about changing the port for smtp.mac.com to 587 (also can impact the smtp.gmail.com use, and I believe they specify using 587).
These are general comments, and are not directed at your situation, but only to detail some things that can be different, and to explain why I can be repetitive about the exact steps taken to Authenticate -- the difference can be very hard to spot.
However, I am still worried about why I cannot ping their SMTP!
Ernie