Perhaps, but neither does it demonstrate that NO Catholics staff them.
What it gets down to is that there is no way anyone can make that claim as they can't substantiate it.
As far as I would go is that it's inconceivable that any true Christian, whatever the denomination, could work at one. If they claimed to be Christian and did, I would certainly have legitimate reason to question the validity of the claim.
This is definitely one rotten fruit by which you may know them.
They are so few and far between that the hysterical antiCatholic press in the US hasn't been able to unearth them. Every time something can be used to put down the Church, the MSM grabs it up and puts it to use.