I only believe it is cromulent to accept a new word in the English language if there is no equivalent word that expresses the same meaning as well. New words such as beclown embiggen our language. From the Urban Dictionary, beclown means:
To make a complete idiot of oneself in public. To behave or speak in such a way, or to make a comment or express an opinion that is so profoundly witless, senseless and obtuse, that you have forever after defined yourself as a person of comical value only. Never to be taken seriously again. Of worth only as an object of ridicule and derision.
Just as to befoul yourself is to make yourself foul, to beclown yourself is to turn yourself into a clown. Beclown is therefore perfectly cromulent. One example given by the Urban Dictionary:
Former Reagan staffer Doug Bandow has also beclowned himself by claiming that the Bali terrorist bombing was in response to Australia's Iraq involvement. Even though the Bali bombing was before the Iraq war.
The only equivalent phrase I can think that arguably captures such stupidity is to hoist oneself by one's own petard. (The origin of this is from Shakespeare and means to blow oneself up - a petard was a medieval explosive, and the etymology of petard is from the Latin word pedere; which means to "break wind".) I think beclown captures incidences such as the example above better, has greater currency and a more obvious intuitive meaning.
In this day and age of "Web 2.0" there are numerous examples of people beclowning themselves. The more recent example that has come to my attention was the expulsion of the biologist and blogger P. Z. Myers from the movie Expelled, which he was in. The real irony and beclowning comes with the premise of the movie, which claims "scientists" who believe in intelligent design are being "expelled" from academia; their rights to free speech and free thinking shut down. You can read about the beclowning and subsequent hole digging, in more than enough detail, in the Wikipedia entry on Expelled the movie.
(One other thing worth drawing a link to is that a serious beclowning event, more often than not, involves some kind of WTF? statement or claim.)