Whilst the above is an interesting report of a real life incident, it is not in my view an accurate picture of what could happen in the much more serious situation of martial law being declared.
Turning out the national guard to assist in any large scale emergency is the sensible thing to do, and a long way from martial law.

Here in the UK, the armed forces were called to assist the civil forces during severe flooding. A sensible and appropriate response and not comparable with martial law.

Here in the UK the government can if need be declare a "state of emergency" which is not martial law, but does give the government greater powers and with less scrutiny than would be the case under normal conditions.

There have been two UK states of emergency in my lifetime, but no martial law.