I actually pngcrushed the result after that just to see how many of the remaining 39 bytes I could get back, but had the same result. PNG has just a smidge more fixed overhead than GIF.
oxipng got it down to 248 bytes. And yes, PNG has a little more fixed overhead, such as the IEND chunk and some of the required IHDR metadata. That only tends to be an issue in files this small, though, and gets dwarfed by potential savings in larger files.
