Does it seem that they stopped caring for her?

First a bit of background:
I have one indoor cat and used to have one outdoor cat. This cat was outdoor because she is extremely skittish and goes crazy when inside. So I would always feed her on the porch steps.
ANYWAYS…
My neighbors (an old couple) love cats. They have three indoor (one is blind and another deaf) so they're very dedicated. They're also very nosy. They told me that my outdoor cat, Myra, is always on their porch and wants attention and that they pet her constantly now. They accused me of being a bad pet owner which offended me because I DO take care of my cat. Now…
One day awhile back I found Myra with a new collar and a new name–Beauty. The old couple told me that's what they call her now. They built her a tree house as well and feed her canned food (I only give my cats dry food). So of course Myra stays there now, sleeping in the tree house, getting fat, her coat getting super shiny, and she's extremely lazy. It always disgusted me because I like my cats to be active and fit but Myra became a queen–numerous cat beds on my neighbor's porch. And everyday I look up to see her snoozing in her tree house. So I let it go, because no use causing an argument if the cat's happy then whatever.
Yesterday I came home from school and found Myra (aka Beauty) on my porch for once. She was extremely dusty and to my surprise she was skinny–skinnier that my other cat. Her skin just sort of hung loose, she looked terrible. She meowed up at me and I got her some food but she didn't seem interested and went back to the neighbor's.
Today I came home and found her on my porch again. She looks even worse. She was meowing up at me and I went inside and got the cat food. I walked out to the neighbor's porch to pour it in her bowl. But the bowl wasn't there. Her food dish were gone and the water dish was filthy.. but the cat beds were still out there so I'm confused. Have they stopped caring for the cat? They've had her under their name for about 6 months. It just seems weird that she suddenly looks awful. :S So what do you think? And nothing has happened to the neighbors, saw them yesterday taking their evening walk…
Thanks in advance.