I believe this was pure spin for the netflix documentary, and not true.
The bigger issue was the reaction of the British government (especially Gordon Brown).
At that time Blair, Brown & co were heavily into their spin & PR, and were jumping on every goodwill campaign going.
Brown turning up in Portugal after only a few days showed this (as it should of been the purview of Millibands foreign office )
Brown & Blair were milking it for all the PR they get, even though the civil servant sent to aid the Mccanns, warned them it might not be a good idea 'to hitch their wagon to this particular horse', as there was massive discrepancies in the Mccanns version of events.