Hate to play the devil's advocate but stakeholders of EASA still have something to lose if the relationship with Qatari goes awry who have a lot of vested interest plus a solid motivation, also non-financial.
EU has painted itself into dependency on natural gas of which Qatar is the largest exporter. Qataris need to keep growing strong to secure their own nation and bloodline future among the dogs in their region. (I personally think those two are actually linked). Own worldwide airline is a powerful tool in the box.
What large EU industries do Qatari already own? I did not research but sure it is much wider than IAG and BAA. Also the non-aviation ones!