You are clearly looking at an example of a person who was clueless about the correct paint to use on the case. There is only one type of readily available paint that works properly to coat plastics.
(but the " who would paint something yellow" question: there is an interesting parallel here; as we age the natural lens in our eye yellows. If too severe it induces some myopia and if goes combination yellow and cloudy it is called a nuclear Cataract. It blocks blue light and alters the color perception. Causing an artist like Monet to paint his paintings colder colors, but after his cataracts were removed, he over-painted a number of them with warmer colors. When the lens is replaced during a Cataract operation, a crystal clear one is generally put in. But a manufacturer came up with the idea of using a yellow tinted lens as a replacement, with an assortment of arguments about benefits of blocking blue light. When I first heard this idea, it stuck me as similar to an Orthopedic Surgeon, fitting a replacement joint that was semi worn out and affected by the equivalent of arthritis. The yellow lens idea never really took off)
Chuck(G) is on the mark. The appropriate stripper to use is Citristrip. It has some other desirable features, it is a relatively benign stripper and not particularly toxic to skin if you wash it off promptly, It washes off in water and appears when I have used it to be relatively non aggressive towards plastics.
Once the old paint is removed, I would not retro-bright it though. I would use Dupli color spray which is excellent for restoring the plastic surfaces to any color you like. It is very fast drying with a highly volatile solvent and it micro etches and fuses with the plastic surface and never separates or flakes. Also it forms a very thin layer and the underlying plastic texture is retained. It preserves the plastic as the years pass, because it largely blocks light. I'm not a fan of oxidative processes/chemicals applied to plastic to bleach it, as I suspect that encourages long term degradation rather than preservation. Also with this remarkable paint, the surface can be made perfectly uniform in color and not blotchy. It actually adopts the surface appearance of the original plastic and it is practically impossible to tell the surface was painted, except by deeply scratching it and examining it with a microscope to detect a color difference at the surface.
. Or Atlantic City. Not that I've ever been to a casino in the 26 years I've lived here. I am hearing good things though.