WHITE SPACE!
I found out the answer was an extra white space that php or as3 was adding in at the end. It could not be seen in the trace statement. I figured this out because I copied the trace statement and noticed there was an extra white space that I could highlight.
In short what looked like the word "success" (without the quotes) in a trace statement, was really the var "success " with an extra white space. Thus the if statement could not see it as "success" because it was really "success ".
To fix it I used this code:
var variables:URLVariables = new URLVariables(event.target.data);
trace(variables.done);
var itWorked:String = variables.done;
var rex:RegExp = /[\s\r\n]*/gim;
itWorked = itWorked.replace(rex,'');
if (itWorked == "success")
{
// Now it works. I hope this helps someone.
}