Strictly speaking, 'toe the line' in this case doesn't make sense either. A runner 'toeing the line' is trying to get as close as possible without overstepping it. The analogy would be if Tim Cook was criticizing the CCP as much as he could without actually crossing them. But he's not doing that, or OP claims he isn't, and that he's doing the opposite, enthusiastically. So even if 'tow the line' is wrong in the sense that's not a recognized idiom, it's more right in the sense that the image of someone pulling weight for somebody else is more like what OP claims that Tim Cook is doing.

Towing the line even has a delightful play on words, where you are towing around the lines out of whatever leaders mouth.

Towing the line, like you are helping to pull along the message. And towing the line like you are carrying around the lines of the message. It's too good to give up for some oddly abstracted analogy about running a race.