> at the start of a phrase it's always 'whether or not X'

I'm confused. Please help me out. What's explained in the site is wrong?:http://www.wsu.edu/~brians/errors/whether.html
“Whether” works fine on its own in most contexts: “I wonder whether I forgot to turn off the stove?” But when you mean “regardless of whether” it has to be followed by “or not” somewhere in the sentence: “We need to leave for the airport in five minutes whether you’ve found your teddy bear or not.”