BBC misinformation?

The BBC have a helpful(?) explanation of the London Mayoral voting system including this:

"1) The Mayoral ballot paper is pink. You can vote for your first choice candidate and also vote for a second choice candidate.

* You do not need to cast a vote for a second choice candidate, but not making a second choice does not improve the chances of your first choice. Your second choice vote gives you the chance of still having a say if your first choice candidate is eliminated.
* If you cast your first and second choice votes for the same candidate, then the second choice will not be counted
* If you only cast a second choice vote and not a first choice vote, your second choice vote will not count."

True as far as it goes but surely they should be pointing out that the only first preference votes that will count are those for Ken and Boris, for all other candidates it is the second preference that will count when their first choice candidate is eliminated. In reality, a second preference vote for Ken or Boris is worth precisely the same to them as a first preference vote. Of course explaining this point might stop some Lib Dems putting Ken as their second preference and would never do, would it BBC?.