Can I choose an encounter if I am unable to complete the clues requirement upon passing the test?
Because order of operations is important and there is an option in the description, the above situation would be a possible way of avoiding a potentially 'bad' encounter.  Since the card is written in a way to say "First, attempt a  check.  Then, you may spend  clues to remove this rumor.", that means that you can always attempt the check as an encounter, regardless of your clue token total.  The card would need to be written differently if it wanted to use clue tokens as a prerequisite.  Something like "If the investegator has  number of clue tokens, they may attempt to remove this rumor as an encounter."  So, yes, you can use this instead of doing another encounter on the space.