If you have a knife with a flexible blade, like a filet knife, I've found it to work better than razor blades. You can grasp the knife handle a little easier I think and depending on the size of the trim, a razor blade may not make it in as far as you need it to break the silicone bond. Just make sure you keep the other hand away from the path of the blade. That goes for using razor blades too.
I've also found it's easier if you can cut through the brace at one point, preferably near a corner. If you have a dremel tool with a cutoff blade, it sails right through the plastic. An angle grinder would work too, but you have to be extra careful with the bigger blade to not nick the glass. Cutting through the plastic makes it easier to get the blade between the plastic and glass to break the silicone bond.
When you replace the trim, remember to re-silicone it. As platytudes suggested, it will make the tank "somewhat" capable of being lifted by the trim, but more important it will prevent rim leaks.
If the tank is full, eurobracing may not be the best alternative since the silicone may not cure properly with the humid conditions. If you can empty it, I'm a big fan of eurobracing, and if you have a good glass shop nearby, that fix can actually be just as easy, slightly cheaper, and a lot better looking than replacing the trim. You do have to be quite meticulous in getting all the old silicone off, even on the edges.
Whichever route you choose, be aware that the edges of the glass under the trim aren't seamed. They are usually unfinished and sharp.
I hope she's offered to pay for the fix! I know I sure would, I would feel horrible about doing that to someone's brand new tank. I guess by the time she smelled something burning, it was too late. 
