Name brand disposable cameras like Kodak cost several dollars more than the off brand disposable cameras. I have seen off brand disposable cameras for as little as $3.99 and name brand cameras for as high as $12.99.
So what is the difference? First, the name brand cameras will come with a more expensive type film. Secondly, They will have a new plastic camera body and a new batter for the flash units.
The lesser expensive off brands of disposable cameras are normally not new camera bodies but the plastic cases of cameras returned for processing of the film. (They have NOT been disposed of, but just recycled.) The off brand companies will bide for a large a number of the returned plastic camera bodies and then they will reload them with film. But many of the camera bodies may be cracked or damaged and they are still reloaded and packaged for sale. These repackaged cameras look great on the store shelf, but will they work? Also they normally do not change the battery for the flash. When you depend on them to get you important pictures you may be out of luck. Many refilled cameras will not advance the film correctly and some will only have enough batter power to take a few flash pictures.
If your pictures are important and cannot be replaced, then to not buy a cheap refilled disposable camera.