Okay, think I figured this out. It's because of how my web.config was set up for forms authentication. Using the forms tag.
The FormsAuthenticationTicket looks at that tag for specific information, and if I didn't create a cookie off of it, it wouldn't authenticate me. This was also defaulted to cookieless mode to UseCookies.
But anyways, after I create a cookie off of that, then I become authenticated and then a new session is created for me. After that, I can then provide any extra cookies I want and let the website use them as needed. But as long as that AuthCookie (in my case .ASPXAUTH) is valid, so is my authentication session.
In fact, when I tried to make a cookie session end when the browser closed, by setting the expiration date to MinValue for the cookie and the ticket, I wasn't able to authenticate either! I had to make the ticket last longer than the actual cookie so that the ticket doesn't expire before the cookie does.
The ticket information is really a configuration used to make the cookie, and after cookie creation, the browser is what defines how the cookies are used.