Yes, your family doctor is also likely part of the 1%. Unfortunately, the term 1% has shifted to basically mean "the people with most of the wealth and power in a country" which is a much smaller group of people, perhaps even less than 0.01%.
Quibbling over the mathematical inaccuracy of the term is tilting at windmills. You'd have better luck getting people to stop using the word "literally" to mean its opposite.
The top 1% are pretty close to having most of the wealth in the US. They have about a third of it. Then 90-99 have about a third, 50-90 have about a third, and 0-50 have a rounding error.
The top 0.1% have about 15-20% of the wealth, which is very concentrated but not a very big fraction of the entire pie. Meaningful cutoffs are tricky to assign.
I don't know how to measure power. You could probably assign a lot of power to the top 0.01%, but in the US they have a single digit percentage of wealth.
Quibbling over the mathematical inaccuracy of the term is tilting at windmills. You'd have better luck getting people to stop using the word "literally" to mean its opposite.