No, the free website does support Safari (Mac and Windows), Internet Explorer, Firefox 3.x and Chrome.
It has been tested under all the browsers, but there are currently a couple instances where logins seem problematic. (However, it's the same login to use the archive and to post here, so I'm a little confused as to how you can post here without first logging in.)
You might also try visiting the logout link, try clearing Safari's cookies cache, and then try logging in again. Jot us an email at support at BigOven.com if you'd like some additional assistance.
(Very deliberately, we are trying to keep our support costs very low, because of our many free services. That's why we like people to first check this support message board before jotting an email support, or else we'd have to raise prices considerably. The vast majority of the time, people's support questions are already answered on the forum, but we do our best to answer them as they come in, publicly, for everyone. Sounds like you're using the free iPhone app and the free website... hope we can get you over the login issues so it's more useful to you!)
Make sure that your Safari browser allows cookies to be written, and that they are not disabled or wiped out by any utilities you may use. I'd encourage you to go into the Preferences area of Safari and delete any existing BigOven-related cookies, restart the browser, and try again.
As for IE, the confusion might have been that Internet Explorer is what BigOven for Windows (our optional Windows desktop recipe software) relies upon. But our free iPhone app uses iPhone Safari, and we do support Chrome, Firefox 3.x (Mac/Windows), Safari (Mac/Windows) and IE.