It does use Mt.Gox in the background for the actual exchange process. There is not enough volume (yet) to make an internal exchange practical, there would be too much risk at the moment, at least for my taste.
When I started on this project, Mt.Gox was pretty much the only choice, because of the large market share (> 80% at the time) and the necessary volume and small enough market spread. Their withdrawal delays are annoying, that's true. It does not affect me directly, since it's only Bitcoin in and Bitcoin out for me, where so far Mt.Gox had pretty much never delays. But it does distort the market price, which means you get a great rate when you fund your Bridgewalker account (because BTC is overvalued on Mt.Gox) and get a bad rate when you spend it (again, because BTC is overvalued on Mt.Gox) - so in the end it kind of zeroes out for you as a user, but it's still confusing for the user, why you have this offset.
There aren't many alternatives though. Bitstamp could be one, but I'm worried that they still might run into regulatory issues down the line. Also none of the other exchanges offer real-time streaming updates about changes to the order book, like Mt.Gox does, which is very useful to keep track of the market. Kraken could be an interesting alternative to Mt.Gox, since they seem to run a solid operation. If they add such a streaming API with real-time updates about the order book and maybe get some more volume, then I would consider switching the backend over.
Or someone else does it first - it's open source now, after all! ;-)
Or maybe you could hedge the whole thing just with some financial swap construction, but I haven't looked into that too much and it's not my area of expertise. I would be interested to find out how much something like that would cost in terms of overhead/fees and who would be a partner to provide such financial services for Bitcoin. If you have some input regarding this, feel free to contact me - my email address is on the Bridgewalker website.