It's not exactly true.
Any power of 2 works. I think 8x8 even, because people make resource packs with this resolution.
So...
2x2, 4x4, 8x8, 16x16, 32x32, 64x64, 128x128, 256x256, 512x512, (this resolutions may hurt client's perfomance), (this isn't possible), (you can't imagine this), , (no "profit" here)
Any square texture works although you're encouraged to use 16x16 or some multiple thereof.