how come some xbox 360's that are modded can still connect to live?

ok so its like this , when i went to asia for a vacation i saw some xbox 360s in a pay to play shop so i decided to play so i could play halo or gears with someone online with my friends in the US, turns out that these xbox 360s are modded but ive heard some people say that i couldnt play on live if the xbox 360 is modded but when i tried to go to live it worked to my surprise, no ban notice no nothing! just like going on a regular non modded xbox , but i did notice something ,when i would play a game like gears of war it would disconnect me from live right away notifying me of an xbox live update , and the update says if i decline the update i cant play games online on live , so in other words the live only works with seeing friends and chatting with them but i cant play with them online, anybody know if this has something to do with that update? do you think that if i proceed with the update, will the 360 get banned or not? pls if anybody knows something bout this please answer =)