From the perspective of an outsider:
Somehow the Goblet of Fire chose Harry Potter as the *fourth* Tri-Wizard champion.
Not everyone, including The Ministry, believed in Harry’s statement about Voldemort’s return.
Harry was the last person everyone knew for sure was with Cedric Diggory before he died. What was the accident The Ministry was talking about, that killed a Tri-Wizard champion?
Sirius Black, whom everyone (except handful of people) thought was Voldemort’s man who betrayed the Potters, killed muggles and his own best friend; the most wanted Azkaban’s escaped prisoner, contacted someone in Gryffindor’s common room through floo network. Umbridge immediately interfered.
Harry and co. founded this obscure, secretive extra-curricular. They said because Umbridge was incompetent DADA teacher. Hermione required everyone who wanted to join to sign their names on a parchment and swear not to tell anyone about it. Even before Umbridge banned all of organizations that weren’t approved by her.
Death Eaters escaped from Azkaban.
Umbridge said Marietta’s mom work in Ministry Department of Magical Transportation, Floo Office. She’d been helping The Hight Inquistor policing Hogwarts’ fireplaces.
Marietta probably knew about Sirius using floo from her mother. I think from above points she would suspect that, of all Gryffindors, Harry most likely was the one Sirius Black contacted.
From Marietta’s pov, Black probably helped Death Eaters escaped Azkaban. Afterall he’d done it before.
What was Harry’s plan with Dumbledore’s Army? Turning the students against The Ministry? Was he trying to be the next Dark Lord? He was also a Parselmouth; Ron said he slayed a *basilisk* in his second year! And who knew what really happened that October night; a baby defeated one of the most powerful Dark Wizards of all time seemed surreal.
So Marietta did what she thought was best. She told the authority.