50% seems a big difference to me, but if you're comparing against a baking tray that keeps the bottom of the cake cool for several minutes, then switching to one that heats through very quickly will certainly mean the cake has less time-to-live in a hot oven before it starts to "burn". If you're only baking for a few minutes anyway then the time the pan takes to heat is a pretty significant part of the cooking process.
As GdD points out, this supposes that the oven is hot enough to burn the cake at all, in the case of them being left in some minutes past the point of being cooked. My experience is that this often is the case in cookie and cake recipes: if you don't take them out they burn. Where I define "burn" to mean any amount of undesired blackening, not necessarily that they actually ignite. Whereas for GdD it violates the laws of physics to bake cake hot enough to burn, so we're either using different oven temperatures or different definitions of "burn".
If this is what's happening then arguably the reviewer should expect there to be a difference between a paper-thin tray and a heavy one. Or, taking things to even more of an extreme, a double-layer tray like Lorel describes in comments. Or, why not: a Pyrex lasagne dish takes time to heat up. You can bake a sponge cake in one no problem, but you're on your own as to cooking time if the recipe is written for a normal cake tin.
The reviewer's failure to predict the inevitable, or belief that thin baking pans are just plain wrong, doesn't necessarily mean that this is not in fact what they observed :-)
As for why the reviewer can't just make the adjustments and stop burning things: if you want the top of it to cook hotter than the bottom then a thin pan doesn't really work whatever you do to the cooking time. That's not often necessary, but maybe they like their brownies crunchy on the top and squidgy on the bottom?
This information may be completely useless to non-British readers, but also when making Yorkshire pudding the gauge of pan can easily be the difference between burning or not, and therefore require an adjustment to cooking time.