Translation:I suoi pantaloni
"Is it the case that the gender of the pronoun only refers to the noun and not the "possessor"of the noun (if that makes any sense)?"
Because of this you can't tell the difference between his or her in Italian. Usually it should be clear from the context which one is meant but Duolingo's sentences don't have a broader context. Instead they accept both his and her on the English translation of every sentence like this... (Even if only one of them is given as the correct translation they still accept both as correct. Or they should. Report it if you find otherwise.)
In real life Italian, if you can't tell from the context whether "i suoi pantaloni" means his pants or her pants, you should use the possessive form of di instead ie: 'i pantaloni di lui' or 'i pantaloni di lei' or 'i pantaloni della donna' etc
Yes, unfortunately it is a problem of interpretation, In the UK 'her pants' could be either singular or plural. Viz: 'Her many pants are in her wardrobe. Plural. ( I was going to write '...in her draws.' but that would have sparked a measure of hilarity.) otherwise, 'She is wearing a nice pair of pants today. Singular
Pants is plural, so you know pants will end in an i= pantaloni. They are HER pants (meaning, plural pants belonging to the third person, because Italian doesn't show us a difference between his and hers), so you know the words for "belonging to a third person, not me, not you" will be one of the two plural options, either i suoi or le sue. You picked "le sue" forgetting that it was a masculine possessive noun, so it has to be "i suoi." If pants were a feminine noun, the plural possessive would use "le sue" -- like if you said "her bananas" it would be "le sue banane." (Right? I think that's right!)
My pants are blue. My pants are torn. "Pants" is plural. A "pair of pants" is not plural because the subject is "pair". "Of pants" further describes the word "pair". This pair of pants is old. That pair of pants has bell bottoms. This pair is great. This pair fits perfectly.