There are a few problems with this line of thinking, but the biggest is- how do we determine whether a child is meeting the "minimum standards"? Standardized testing doesn't work when you're not teaching the curriculum from which the standardized tests are being derived.
For example, my 10 year old uses a math curriculum that doesn't follow the same scope and sequence as a traditional public school curriculum. So, he's doing pre-algebra and pre-geometry, but we haven't covered order of operations and exponents yet. Well, most 5th graders in public school have covered order of operations and exponents, so even though my son excels at math, he would not score well on those portions of a typical standardized test.
History is another good example of this. I teach history chronologically. So, while my 5th grader could run circles around his peers in ancient history and early American history, he knows very little about recent American history or Texas history. But, his public schooled peers all took state history in 4th grade, so they would pass that portion of the standardized testing while he would fail.
Standardized tests that are written to coincide with public school curriculum will never be an accurate barometer for success or failure of home schooled children.
All that to say, it's pretty easy to tell whether or not a child is being educated without the use of standardized testing, and the child in the OP clearly is not being educated.