If by "lie", you mean say that they don't know when they do, I suspect they can. The alternative is to say something like "Yes, they're distressed" - which they can't do - or to say "I know but can't say" - which is as good as the same.
My understanding is that a clause would not be needed because the vendor would usually have to have the permission of all the mortgage holders prior to accepting an offer.
But that doesn't stop vendors doing the wrong thing, so I get why you'd want more protection than that. You could...