It's a real bank. Luxembourg has cheap corporate tax rates, so all Paypal's Europe stuff goes through Luxembourg and thus they get cheaper taxes.

Just because it is called a bank does not mean you'd would want to rely on it. If Paypal suddenly decided to pull up it's stakes and take all it's customers money, I would not imagine that Luxembourgois banking law would help a lot of customers.

Do you have any sources confirming that the Luxembourgish banking laws would allow Paypal (and all the other countless international banks stationed there) to get away with this?

Because Phoenix is known for its important education sector just as Luxembourg is known for its important financial sector?

I am very confused by your statement.