Hi BPB!
Stick to your own breakfast! It is similar to my own, light before exercise and a bit more filling afterwards!
The guy who said working on an empty stomach speeds up the metabolism needs to go back to the books. After a nights sleep your body is carb depleted. If you exercise without refuelling you will force your body to work on its alternative fuel system - your lean tissue (muscle)!! Yes your metabolism will be raised, but at what cost?
The absolute basic info here is that FAT can only be burned as a fuel in the presence of CARBs - just like the CARBurettor in your car engine has to add oxygen before the petrol will burn! This is a non-negotiable part of our physiology. You may well lose more weight by not eating first but the weight you lose is the usefule bits of your body, not the excess fat you really want to get rid of.
This is part of the reason that the Atkins diet, and any other low carb diet, are of questionable long term usefulness or safety!
I hope this helps. It should also help you feel confident in your own assessment of health/exercise info. You obviously suspected the Discovery info, and you were right to. Sometimes exercise experts are only expert in getting results at speed, not necessarily safely and over the long term. Others are expert in sport info, which is completely different form health and exercise info.
Keep on keeping on, Stef