By reason of geography, PLAN's SSBNs has to move past the SCS area otherwise they would be very restrictive in the areas of operations and high risk of detection from sensors, sonobouys, SSKs and SSNs. regardless of depth or even thermoclines in the SCS.
The best 'safe passage' to break into the Pacific would be the Luzon/Kyushu gap but that area is littered with SeaWeb undersea array and a host of other sensors not unlike the ones put in the GIUK gap but likely more modern and advanced. That route also takes them far away from mainland air defence and other assets.
On 5 March 2009, the USNS Impeccable was in the SCS very very close to Hainan Islands. Obviously the reason given was monitoring sub activity however ships like that do and can lay undersea sensors and detection arrays. I'm not saying she did but she got buzzed several times and even threaten however I can understand PLAN's concerns.
If PLAN ships are laying undersea sensors and arrays 70 miles off Groton, Bremerton, Kings Bay etc I would presume the USN would be a tad paranoid as well.