It's more accurate to say the 3rd party doctrine goes around rights, not just legal requirements. The 3rd party is forced to betray its clients to the governmen

It's more accurate to say the 3rd party doctrine goes around rights, not just legal requirements. The 3rd party is forced to betray its clients to the government, even against its will. In other words, this doctrine doesn't only let government agents do something they otherwise wouldn't be allowed - it also lets them force others to do something, pressing them into government service.