Importing complex xml into a DataSet

(A prolific PowerShell poster suggested I come over here....)

I have a schema but it doesn't import correctly into a DataSet with the expected table names.

There is more but I think if this gets solved the rest will, what am I doing wrong with the table names?

My PowerShell code (actually, the same thing happens with c#):

clear-host

$dsXml = new-object "System.Data.DataSet"
$dsXml.ReadXmlSchema("C:\temp\xml\mySchemaTest.xsd")
$dsXml.ReadXml("c:\temp\xml\myXmlTest.xml", 'ReadSchema')


Write-Host "Table names in dataset"
Write-Host "======================"
foreach ($table in $dsXml.Tables)
{
	Write-Host $table.TableName
}

The schema (tested as valid)

<?xml version="1.0" encoding="utf-8"?><xs:schema xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
attributeFormDefault="unqualified"
elementFormDefault="qualified"
xmlns:xs="http://www.w3.org/2001/XMLSchema"
xmlns:msdata="urn:schemas-microsoft-com:xml-msdata"><xs:element name="products"><xs:complexType><xs:sequence><xs:element minOccurs="0" name="books"><xs:complexType><xs:sequence><xs:element minOccurs="0" maxOccurs="unbounded" name="item"><xs:complexType><xs:sequence><xs:element minOccurs="0" name="title" type="xs:string" /><xs:element minOccurs="0" name="pageCount" type="xs:string" /><xs:element minOccurs="0" name="price" type="xs:integer" /></xs:sequence></xs:complexType></xs:element></xs:sequence></xs:complexType></xs:element><xs:element minOccurs="0" name="fruits"><xs:complexType><xs:sequence><xs:element minOccurs="0" name="item"><xs:complexType><xs:sequence><xs:element minOccurs="0" name="type" type="xs:string" /><xs:element minOccurs="0" name="color" type="xs:string" /><xs:element minOccurs="0" name="price" type="xs:string" /></xs:sequence></xs:complexType></xs:element></xs:sequence></xs:complexType></xs:element></xs:sequence></xs:complexType></xs:element></xs:schema>

result (I only expected 2 tables, all my data is actually in the table "items" in an all messed up way):

ReadSchema
Table names in dataset
======================
books
item
fruits