Since no one can prove which side of the story is correct, then you can simplify the situation by looking at it using only the facts you know.
Reasons to support Saadia:
-She has broken no known laws of either Skyrim or Whiterun.
-She is currently a peaceful and productive member of the community.
Reasons NOT to support Alik'r:
-They are a group of seemingly hostile foreign warriors (emphasis on foreign... Skyrim doesn't play well with others).
-They are going around causing disturbances across Skyrim and Whiterun Hold in particular.
-They made their temperary base of operations with a known group of bandits.
-Regardless of what laws or rules Saadia may have broken elsewhere, Skyrim authority is under no obligation to cooperate with a foreign matter or investigation. Even if she broke the laws in a different Hold within Skyrim, Whiterun authorities aren't obligated to recognize the charges.
-No official request was made to higher authorities, either the Jarls or Imperial representatives, to detain Saadia. Rebels or not, their fight(s) aren't your problem.
-One warrior was even caught sneaking around where he shouldn't have by Whiterun guards, so their reputation is made even more questionable.
Considering all of these facts, the Alik'r warriors should be treated as a threat to the peaceful people of Skyrim. It really doesn't matter what Saadia did or didn't do. As a Skyrim citizen, she should be fiercely defended.