No, I don't think it's wrong at all and I would do the same thing. I have a very similar situation where I live and I have taken in several cats and a dog that the neighbors just won't take care of and yes I got them fixed and now they are mine. The cats come to my house and they are hungry, so I feed them. The neighbors don't care about the animals and that makes me furious.
This last episode happened earlier in the year when the neighbors got a new kitten. The kitten would come to our house and of course we would feed her. Winter came and it was cold outside so my husband and I made the kitten a bed outside. We had considered bringing her inside our house when it was cold, but we already had 3 inside cats and after all, it wasn't our cat. If we would have known what was going to happen, we would have brought her inside. Anyway, one morning my husband and I had to run some errands and when we got back, the kitten was in her bed outside our door, shivering and bleeding. It was 16 degrees outside that morning. We immediately brought her into the house and she would not come out of her bed. She finally warmed up and we coaxed her out. I do not know what happened to this poor kitten, but 3 of her 4 legs were injured. Her front legs each had a large patch of fur missing and the skin was totally ripped off of one of her back legs and foot. To make a long story short, my husband and I doctored on her and healed up her injuries and she now stays inside the house with us. The neighbors eventually moved away but they never did ask us if we had seen their kitten. If they would have, I would not have given the kitten back to them anyway.