Magento Product Collection – Get All Products by Category ID

You are directly operating on Zend_Db_Select which is always a bad idea.

The thing here is, that getLastPageNumber is using getSize, which is \Varien_Data_Collection_Db::getSize and uses \Varien_Data_Collection_Db::getSelectCountSql which is overwritten here \Mage_Catalog_Model_Resource_Product_Collection::getSelectCountSql and implemented with \Mage_Catalog_Model_Resource_Product_Collection::_getSelectCountSql.

Digging deeper in this methods shows:

protected function _getSelectCountSql($select = null, $resetLeftJoins = true)
{
    $this->_renderFilters();
    $countSelect = (is_null($select)) ?
        $this->_getClearSelect() :
        $this->_buildClearSelect($select);
    $countSelect->columns('COUNT(DISTINCT e.entity_id)');
    if ($resetLeftJoins) {
        $countSelect->resetJoinLeft();
    }
    return $countSelect;
}

And I assume your problem is:

    if ($resetLeftJoins) { // true by default
        $countSelect->resetJoinLeft();
    }

If you want your collection to include the inventory information, there's a flag you need to set before you load the collection.

$productCollection->setFlag('require_stock_items', true)