Expected behavior. LSB applies to properties, but in PHP it was decided to have static properties shared between classes and their subclasses (via a reference set), possibly so that they can reliably be used in a non-static contexts. This behavior can be changed by redeclaring the property or manually breaking the reference set (possibly this ought to be documented).

you are correct in your statement about breaking the reference, the following 
example works as i believe should be default.

<?php

class old {
	static $prop = 'old';
	public function __construct() {
	
		static::$prop = &$this;
		// ^^^ daft assignment of any random reference to cause it
		// to break itself. normal assignment will not do it has to 
		// be a reference. comment out that line and instead of
		// "old one two" you will get "two two two"
		
		static::$prop = get_class($this);
		// ^^^ an actual assignment that i care about keeping.
		
		return;
	}
}

class one extends old { }
class two extends old { }

$one = new one;
$two = new two;

printf("value: %s %s %s\n",old::$prop,one::$prop,two::$prop);

?>

nice and jenky.

Changing this behavior would be a BC break; consider:

<?php
class A {
	public static $f = 7;
}
class B extends A {
	function m() {
		A::$f = 6;
		return self::$f;
	}
}