Migleader, the Americans are not the only party who would be embarassed, it take two ships to collide.
"beijing would then probably accuse amnerica of purposely staging the collision to damage the sonar"
I wasn't aware Beijing was populated by complete idiots. Such an accusation would gain nothing but laughter. Why on Earth would America want to damage a Chinese sonar (that is not onlt likely fairly obsolete to America, but could be replaced with ease).
"and make some monay by making the u.s navy pay for the damage to 167 and its sonar."
Why would America be paying for the damage?
You seem convinced that America is the party in the wrong. Don't forget that the instance is two vessels becoming entangled, in international waters. It is the Chinese vessel in the wrong, if they try to tow the American boat to Chinese soverign waters, and especially if they fired upon the American crew.