When handing over the responsibility of training pilots to some entity inside another entity, like layers of an onion, it means you outsourced it into a black hole of regulation and competence. That structure is made to specifically obscure what these "cost saving" measures actually imply.
When we're talking about this kind of critical activities you want them happening somewhere where you can actually hold people accountable. Somewhere with visibility, transparency, and working judicial and legislature.
And where would that be?
If the USA's (or wherever) justice system can be bamboozled by off shoring liability, that's indicative the system is broken and / or the necessary treaties are intentionally absent / weak.
"According to union officials, CCL’s ownership structure is a company within a nest of shell companies"
Yep ... it must be the scenery.
Company outside the US? Likely a dodgy company.
Pilots potentially not American? Likely dodgy pilots.
What do you think the US does so differently to everyone else that means outsourcing the work will be worse quality?
Did the article say Boeing is outsourcing pilot training to Pakistan?