Syria does not need to formally apologize for downing of the fighter jet because this jet was flying deep in Syrian airspace and any other country would have done the same. This was after all a "Fighter Jet". The only reson an appology is requested is due to the fact that Syria is not an ally of either America or Israel. If Turkey or any other pro-American country would have shot down a Syrian jet, no appology would have been requested and Syria would have been blamed for flying deep into Turkey's airspace.
Saudis warns U.S. that 9/11 responsibility law would erode investor confidence in America (Reuters)
from the article: Bodies of two Turkish pilots shot down by Syria recovered from seabed