You could play pirated games online with the 360. The piracy was at the DVD Rom firmware level, replacing the stock firmware with one that basically changed the book type of the media. (And in later versions also mimicked other security checks preformed by the console to validate the authenticity of the disk)

However the DVD firmware mod didn’t break any digital signatures. It just allowed signed code to be executed from unauthentic media, so it only allowed piracy/backups not a full jailbreak allowing unsigned code. That was more the jtag/reset glitch era. Which was more “offline only” as it was easier for MS to detect and ban your key vault from Xbox live, but because people were willing to pay for modded lobbies in games like Call of Duty (which allowed you to rank up much faster) and Xbox dying if you sneezed that them, there was a even a market for extracting the keys from dead consoles to sell to those selling modded lobbies.

You still ran a risk of getting your console hardware banned for doing the DVD firmware mod, but towards the end I believe MS threw in the towel (even after trying to embed the flash chip in the samr package as the DSP for the drive which resulted in the kamikaze hack before the drive got further exploited) because one method they tried to use to detect piracy had such tight tolerances that it caused legit customers with aging drives to be caught up in the ban wave and MS had to walk it back.

The head of Xbox security (who sadly is no longer with us, he was a good egg at heart) left Microsoft not long afterwards. Obviously stating he wanted to move on to other things, but the word around the community at the time was that he was shown the door.

Personally I don’t hold much to that story (of him being pushed), this was so late in the consoles life that it seemed like it was trying to patch the hole in the titanic after it already sunk.