I’ve never heard of anything quite like what you’re asking.
Note that the developer isn’t actually using Weather Underground. They must have changed it to OpenWeatherMap and not fully updated the titles/descriptions:
If you’re already using OWM for openHAB, then I’d suggest it doesn’t make a difference if the data goes directly from OWM or through OH. The source remains the same.
But I can get why you’d want to pass it through OH if you’re using a different weather source.