Will their rosters be analysed as a matter of course to asses likelihood of fatigue
The roster will be analysed and assessed as "legal" and the poor crew member will be hung for not managing their rest appropriately. Don't mention the "F" word. This will create a problem with the FRMS approval.
Does **** have a fairly robust internal investigation process?
Yes, this is commonly known as the "Just" culture. That is, Just sack em and upper "management" Just cover thy ar*e at all cost.