Syrian Jet Shot Down - But why exactly?

Part 1 of ...

On June 19th the United States shot down a Syrian warplane for the first time in the Syrian conflict.

Russia have responded aggressively - claiming the Syrian jet was only attacking ISIS forces.

The US have countered this - claiming the jet was attacking Anti-Syrian Govt forces.

But which one is true?  The US or Russian official lines; or perhaps both?

The Fox News take was that the Syrian Jet was bombing forces backed by the US - but what does that mean? 

Why are these 'US backed forces' only ever referred to vaguely - why don't we get specific information about who they are? In the beginning I thought this was suppose to be the free Syrian Army but now these groups are termed labelled as 'Rebels' or 'Anti-Assad forces' etc.  

Is it possible that the US would want Assad gone more than it wants ISIS defeated?  And who would either of those outcomes actually benefit?

Of course it's hard to really know - but I doubt governments would want to tell outright lies in these types of incidents - they usually just avoid the exact truth - instead preferring to be vague, but not strictly inaccurate.  

If that's the case in this instance then the U.S. version raises more questions than it answers.