The flip side of this is from the professor's perspective: some undergrad in every class will lie their ass off about why their assignment was delayed.
Unfortunately, this reality produces no good options if you think someone is telling the truth: (1) make an exception, and be unfair to the rest of the class or (2) don't make an exception, and perpetuate unfairness for the impacted student.
Note that AI provides a whole new range of possibilities for automating lying about assignments.
Unfairness to the class, if kept under wraps, is a case of no one actually being harmed.
Option 3: treat your students like adults as much as possible and be flexible with everyone about how they complete the class as long as they demonstrate that they've done sufficient work and have sufficient mastery of the material. Then you don't need to play arbiter about whether having a child in the hospital is a better excuse than having their backpack stolen, and you don't unfairly favor squeaky wheels over meeker students.
That's fair, but in this case it should be pretty easy to verify if the person is lying. The claim is highly reproducible and the instructor wouldn't even have to do it.