BTW, my E-J dictionary says the same, but on second thoughts, I wonder if there's a subtle difference: downplay means 'he knows its important but says not', while 'play down' means 'it's not so much he knows the importance as that he missed the importance'.
No, I don't agree. I think both versions of the expression indicate a deliberate attempt to persuade people that X is of very minor importance.
I don't feel that the expression deals at all with whether or not the speaker is being deceitful. He may downplay X because he believes false rumors are spreading claiming X is a very big deal, and these rumors are bad for