Yes, this is correct. Although it is capable if switching, this would cause problems that require a motherboard fix which is not implemented, so the machine runs big endian in practice. I included a wikipedia link to explain.
All current software does this, but the switching capability means the motherboard could be modified to allow it to run little-endian. This means that if someone wanted to repurpose old Xbox hardware to run a little-endian operating system it would be entirely possible. Certainly not a practical process considering the cheapness of CPUs, but it could make for a fun experiment.
It's possible, but also keep in mind that the 360 chip was a custom PowerPC, that had high manufacture numbers. It's entirely possible that the little-endian functionality was somehow broken to save money or otherwise.
But the point was originally about what the Xbox360 runs, and before that, how it affected development. Not about what the silicon in a particular chip in the 360 has the capability of doing.