Neighbor severely neglects their cat

UPDATE!!! Kitty is just very old (20 years), not neglected. I’m so sorry LOL, giant false alarm. Very relieved though. Big lesson learned in my rescuing career! Full update https://www.reddit.com/r/CatAdvice/s/y2MzviZEzw

Hi everyone, I am new here but need some advice as a cat lover bc I am conflicted morally. I was on a walk in my neighborhood with my husband a few nights ago and saw a cat, which is not unusual because I live in a very safe and quiet neighborhood where a lot of people have indoor/outdoor cats. I wouldn't ever personally put my cat outside, but I digress. It approached us and I was excited that a cat was going to give me the honor of petting it lol. However as it approached I realized it's long black fur was severely matted. it was limping, and when I pet it I literally only felt its spine. SO skinny it made me weak in the knees.

My husband ran home to get cat food, and I stayed behind to pet it. A neighbor was outside and I asked about the cat, he made a face at me like "yes I know that cat is neglected" but pointed to the house it belongs to. He said he feeds her himself because of how skinny she is. I then saw the owner approaching walking her dog, and the cat ran after her owner, who didn't even glance at her before going inside and slamming the door shut. It KILLED me.

So I have a vet appt scheduled for her today. I went back last night to feed her and she was sitting on their porch begging to come inside. It looked like the family was packing for vacation? In and out of the house but nobody acknowledged her, except their son who said "hi (cat's name)". Somebody even at one point picked her up, but just to move her away from the door outside. So clearly this is their cat, they interact with her, but don't care for her?

I rescue cats, so does my mom. I could EASILY find this beautiful cat a loving home (if there is no microchip) inside where she clearly wants to be. But guilt is eating away at me that this cat belongs to someone... help!