Can I avoid falling in the rain on a corner?
16 km/h is so slow that even the worst tyres should keep you up, unless something like oil spills were involved.

If something is so slippy that you fall without warning at such low speeds there is not much one could do. If you have a hunch this might happen tripodding corners or getting off the bike may help.

The first drizzle after a long dry spell can leave a very slippy mix of wet dirt on the tarmac. It sometimes feels almost like soap. More intense rain washes it off quickly.

Some surfaces (eg metal or road markings) can get slippy when wet. Avoid anything that looks smooth and wet. edit: The smooth tar of the patched cracks visible in your photo are also example for such treacherous surfaces.

If temperatures are closer to zero black ice may form spontaneously. It is nearly impossible to distinguish from wet road and is extremely slippy.