I don't see much wrong with that. It's a transformer with a primary and a secondary - you feed the signal in at the top of the primary and connect the bottom of the primary to ground. Then the signal goes through the core to the secondary. You connect your coax braid to the bottom of the secondary and the signal comes out at the top to your coax centre wire.
Just like this...
Now whether you connect the ground to the coax has always been a matter of opinion - my best answer is "suck it and see"!
You have three choices...
1. Connect the coax braid and the secondary bottom to the local ground.
2. Connect the bottom of the secondary to the local ground but don't connect the coax braid to anything - except the receiver of course.
3. Don't connect the secondary to anything except the coax.
My system works best with solution 3 - but it's not a Beverage - just a longish wire.
If you know anyone who has been suckered into buying one of those PAR SWL antennas, then the UN-UN box they supply has three terminals to allow the braid to be connected anywhere as above.