Why homeschoolers feel that e-schooling is not homeschooling?

Last night I was searching something about early childhood education, educational activities and difference between homeschoolers & e-schooling. I have gone through few article and I got Mindy Brems article, maybe she has written good content. According to her E-schooling is actually a form of public school, with certified teachers for each online class that is done via the Internet in the home setting.

Mindy Brems of Coshocton chose to educate her three children - Emma, ninth-grade; Ellie, sixth-grade; and John, fifth-grade - through an e-school two years ago. She researched the various home school and e-school programs before deciding on the option they are currently using.
"With the e-school program that we use, Ohio Connections Academy, we are following the state's curriculum which meets all the educational standards set by the State of Ohio," said Brems. "That also means that my kids take all the tests required by the state."

Brems feels that the confusion between homeschooling and e-schooling comes from the fact that many e-schoolers tend to call themselves homeschoolers, but technically that isn't correct.
"Many traditional homeschoolers feel that e-schooling is not homeschooling," said Brems. "And for the most part they are right. Homeschoolers fought for 30 years to have the right to educate their children at home without the state's interference. So it is different from e-schooling. E-schooling uses the state's public school curriculum."

So I am asking you what is your suggestion on Mindy Brems's Article and major difference between homeschooling and e-schooling