No.
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soheil1being only too happy to ..."Only too happy to ..." is an idiom that means being sincerely and/or enthusiastically willing to (do something).
and in other places.
But it seems that despite her feisty demeanour, Courtney Love is only too happy to pose with fans.
soheil1It seems to have been used here that wayThat way? What do you mean by "that way"? Which way? Do you mean as explained in the link? If so, then you should note that in that post (if I have located the one you're referring to), it says "which others think they might not enjoy".
soheil1I guess he meant the person is making an exception of himself in enjoying that activity.Even if he did, the exceptional idea is conveyed by 'despite'. not by 'only too'. This sentence is perfectly natural: