The word "Bitcoin" has become tainted within culture. Bitcoin is commonly associated with things like Silk Road, MT Gox, ect..all sorts of scandals. So, when marketing bitcoin, people are now talking about "blockchains" and not "bitcoins"
kind of half right..
but its more about people who used to talk about bitcoin the technology/protocol and bitcoin the currency without defining the difference.
so the word blockchain is for the technology/protocol. and bitcoin is the currency..
now onto the OP's point.
banks cant own bitcoin.. as ~15mill coins out of 21mill are already in peoples hands so they cant really control it..
however starting their own altcoin currency using the blockchain technology allows them to have their own controls on a limited supply asset, which they can premine/sell at their pleasure.
now the way i see it.. although you may think of a bank as a single entity.. the banking industry do not want a single employee to defraud the system, so although as a industry they are not good.. within the industry they dont want the individual employee's getting rich from it.. so its in their interest to have 500+ nodes scattered around in 500 undisclosed locations all equally mining the same chain, purely for their own internal security..
just imagine how much they would save on not needing to have internal fraud squad, security guards, and double audits..
that alone would save them many millions of cost in labour and time.