In addition the video doesn't understand what the colonial militias were. They were not U.S. militias as there was no United States, they were British militias organized and manned by British citizens of the North American colonies as a supplement to the British army. The militias were only open to free males, not women, not slaves and their organization varied from colony to colony and town to town.
The war for independence started when a group of British militia men rebelled against their own government, they weren't Patriots yet, they were secessionist, rebels who were orchestrating an illegal uprising.
We now call them patriots as the right of independence was secured...but at the time they were revolutionaries. Similar to many such groups we see in the world today.
The example given of women is misleading. Women were not part of the militias, they may have taken part in the revolution, but not as militia members. That's why Deborah Sampson removed the musket ball from her leg herself. She was afraid it would be discovered that she was a women masquerading as a man. As a woman she was not eligible to join a militia. Which she didn't. She disguised herself as a man and joined the 4th Massachusetts Regiment, a part of the Continental Army.
The first American militias were formed by the Article VI of the Articles of Confederation:
...every State shall always keep up a well-regulated and disciplined militia, sufficiently armed and accoutered, and shall provide and constantly have ready for use, in public stores, a due number of field pieces and tents, and a proper quantity of arms, ammunition and camp equipage."
They were not necessarily well armed as there were not a lot of guns in the colonies at the time:
"The militia are turning out with great alacrity both in Maryland and Pennsylvania. They are distressed for want of arms. Many have none, we shall rake and scrape enough to do Howe's business, by favor of the Heaven."
Most of the arms used in the war came from France. France supplied uniforms, boots, arms, cannon and 90% of the gunpowder needed.
The war was largely fought by the Continental Army and the French not the militias, the militias were more of a local police force. All the while France and Spain were attacking Britain on other fronts.
After the war the militias were used to put down rebellions, not lead them as in the case of the Shay's and Whiskey rebellions.