Maybe I'm looking at it from the wrong corner, but actual money transfer is such a minor part of finance that the comparison is akin to "Internet Protocols has democratised Computer Science".
I guess what the NS is trying to say is that there are a lot of services that at the end of the day require money transfer (like bank account, credit card, escrow, ...). Until now such services needed to be backed by an underlying financial institution since there was no way to transfer currencies safely without them.
Now with Bitcoin, there is an infrastructure that is free to use. Theoretically, using that infrastructure, you could create banking service outside the traditional infrastructure (messaging networks, clearing houses, settlement banks, ...)
However, all those institutions bring a lot more services on top of money transfer. The internet revolution was the opening of networks, rather than HTTP itself. So Financial institutions acceptance, rather than public recognition really matters if that comparison is to hold. Right now, Bitcoin and other crypto-currencies are treated as a new type of asset, it is far from making any progress in the infrastructure side.
And of course, the elephant in the room are the regulations. The world is still recovering of the last financial crisis, the world mood is not really looking forward to less regulations. The best that can be hoped right is for Bitcoin to dodge regulations and become de-facto currency, rather than actual currency. IMO that would be a criminal-smelling loophole left there by the various regulatory institutions. Because let's face it, even with regulation, large financial institutions like HSBC have no trouble laundering drug cartel money, so they are the one that will most benefit it, not some startup in the Valley.