I think the couple are assuming a level of probity and conscience on the part of the tabloids which, by definition, they have never had and never will have.
To approach an organisation which makes its money by taking the 'truth' and bending it beyond recognition for a readership who would believe that the earth is flat if the Sun or Mirror headlined it, and assuming you can either bargain for its good side, or withdraw, as they are doing, and assume it will mean they will only print the truth, belongs in fantasy land.
To think that the tabloids will stop printing garbage because it is not 'directly' from the couple, or that the readership will cease to read and believe lies because they couple have not 'authorised' a story is to believe that the tooth fairy lives on the moon which is made of green cheese.
This is the media. They make money from piffle, tosh, lies, half-truths, made-up garbage and self-created scandal.
To assume you can control them, bargain with them, agree with them, make a deal with them, co-operate with them, or, and this is the real stinger - withdraw from them, and expect them to behave any differently, is to be so naïve as to ponder if you should be allowed to use sharp cutlery.
Actually, the media will behave differently.
Without the pretence of co-operation and agreement, the media will go full speed into revenge and destruction, unfettered by any pretence of worrying about future co-operation, because there is none to lose, so the media have everything to gain by destroying what is left of the couple's reputation and popularity.
Watch the papers over the next few weeks - it's open season now.