US is apart of NATO and that meant nothing during the capture of the USS Pueblo and countless other situations. Generally many NATO nations would be hesitant if Turkey asked for a war over its military aircraft getting shot down while violating Syrian airspace. It’s also very important when conducting military operations in a area to have communication with others that have military forces in that area to avoid confusion and unnecessary conflict. similar to Iran calling Iraq to inform them that they are about to hit a US military base in Iraq. So Turkey’s request is also informing Russia that they are attacking a mutual opposition and not Russia or Syria, so saying please inform your people on the ground so they don’t freak out and get trigger happy.