PHP Inheritance and Static Methods and Properties

No. That's not true. Static Methods and properties will get inherited the same as non-static methods and properties and obey the same visibility rules:

class A {
    static private $a = 1;
    static protected $b = 2;
    static public $c = 3;
    public static function getA()
    {
        return self::$a;
    }
}

class B extends A {
    public static function getB()
    {
        return self::$b;
    }
}

echo B::getA(); // 1 - called inherited method getA from class A
echo B::getB(); // 2 - accessed inherited property $b from class A
echo A::$c++;   // 3 - incremented public property C in class A
echo B::$c++;   // 4 - because it was incremented previously in A
echo A::$c;     // 5 - because it was incremented previously in B

Those last two are the notable difference. Incrementing an inherited static property in the base class will also increment it in all the child classes and vice versa.

No (Apparently I couldn't see the not in the question). public and protected static methods and properties are inherited as you would expect them to be:

<?php
class StackExchange {
    public static $URL;
    protected static $code;
    private static $revenue;

    public static function exchange() {}

    protected static function stack() {}

    private static function overflow() {}
}

class StackOverflow extends StackExchange {
    public static function debug() {
        //Inherited static methods...
        self::exchange(); //Also works
        self::stack();    //Works
        self::overflow(); //But this won't

        //Inherited static properties
        echo self::$URL; //Works
        echo self::$code; //Works
        echo self::$revenue; //Fails
    }
}

StackOverflow::debug();
?>

Static properties and methods obey the visibility and inheritance rules as illustrated in this snippet.