Those weren't TV cameras hooked up for the sole purpose of getting her rescue filmed. All spec ops use those video feed systems for command and control purposes so the folks running the show can see what the shooters do. No different than gun camera footage in fighters and bombers. It's used as an intelligence tool.
That the Army decided to release the footage, without commentary, so that the good news about her rescue can be seen by all, was not some Machiavelian propaganda move.
All of the stuff about what did or did not happen during the firefight was based on eyewitness accounts (inaccurate as they turned out to be), by those members of the convoy that escaped capture.
"In war nothing is ever as bad, or as good, as it is reported to Higher Headquarters. Any reports which emanate from a unit after dark — that is, where the knowledge has been obtained after dark — should be viewed with skepticism by the next higher unit. Reports by wounded men are always exaggerated and favor the enemy." - General George S. Patton, War As I Knew It. 1947.
"The report of no incident that happens after dark should be treated too seriously. They are always overstated." - General George S. Patton, War As I Knew It. 1947.