Are laws facts?

If a natural law summarizes data, and the data are facts, isn't a law a fact too?

No. A law is a description of the data.

If new data comes to light that violates the law, it must be amended or discarded.

Because laws usually are based on a vast body of data, gathered over a long period of time and reviewed by many investigators, it's very rare for a law to be discarded.

It does happen, though. For example, until 1956 all evidence indicated that processes involving elementary particles would be essentially unchanged when the directions of the particles were replaced by their mirror-image directions.

This "law of conservation of parity" was disproved when an elegant experiment performed by physicists at NIST showed that the mirror-images of a process were in fact distinguishable.

See The Fall of Parity at NIST's web site for an account of the experiment.