You do realise the players do not fill out this documentationI believe (and could be wrong) that the players from the UK did not declare that they arrived from the UK but lied about their original Country of origin.
If true it's falsification of a travel document, it's not for the Brazilian authorities to trace where they came from it's the fact that allegedly those players lied.
If this is true it's the players and their advisers that are inept.