It is
(a) unlikely that she is sending her son to the one private school in Eastleigh. A few miles up the road you have www.winchestercollege.org/ for example.
(b) unlikely that her son was offered a place at the top state school in Eastleigh.
According to this:
www.school-portal.co.uk/GroupDownloadFile.asp?GroupID=25437&ResourceId=406613
the catchment doesn't include any of (rather grotty) Eastleigh at all, but rather the leafy and expensive Chandler's Ford - the catchment conveniently excludes all the lower quality housing on the other side of the M3.
A quick look on Rightmove shows houses at £535k summarised as
"APPROX 1/4 ACRE PLOT- Much improved detached family home set within mature gardens. Thornden School Catchment"
Another at £520k listed as
"The property is within Thornden School catchment. "
Meanwhile in actual Eastleigh, there are lots of houses like this:
www.rightmove.co.uk/property-for-sale/property-22391076.html
A similar house in the catchment for this so-called Eastleigh school are nearly twice as expensive:
www.rightmove.co.uk/property-for-sale/property-37161043.html
Fact is that parents (those who can afford it) pay tens or hundreds of thousands of pounds for access to better (read: those without many poor people) state schools, yet get all high and mighty about those who are upfront about this process and simply pay the money directly to the school rather than some blood-sucking estate agent.