Biff wrote...
....
Easily fixed using either your modified suggestion or:

=INDEX(Version,MATCH(MAX(IF(File_Name="Test File 1.txt",
Date_Val)),(File_Name="Test File 1.txt")*Date_Val,0))

which you could reduce further to

=INDEX(Version,MATCH(MAX((File_Name="Test File 1.txt")*Date_Val),
(File_Name="Test File 1.txt")*Date_Val,0))

I'm not comfortable using that Lookup technique just yet. I don't fully
understand how to test for multiple criteria.

If the multiple criteria would always result in a single entry
satisfying the criteria or all matches would be equally acceptable,

LOOKUP(2,1/((CriteriaExpression1)*(criteriaExpression2)*...), ReturnValues)