There is a newer thread also related to this discussion Fresh Tracks.
I asked about an official answer regarding both threads and received this which I post here as well:
You cannot play Fresh Tracks to cancel any effects on an enemy just revealed from the encounter deck because it doesn't trigger until after that enemy is added to the staging area.
To address your examples:
-Eastern Crows will already have been revealed & triggered surge before it is added to the staging area.
-Wild Bear will trigger it's Ambush keyword "when it enters play" whereas Fresh Tracks can only be triggered "after an enemy is added to the staging area" so the Fresh Tracks cannot prevent the Wild Bear from making the engagement check because the "when" effect must be triggered before the "after" effect.
(Edit: Link above)