Change the line
sbit LED_pin = P0^0;
to
sbit LED_pin = P0^7; /* can be 0..7 bit number */
and run it again, and see what the P0 display does.
{assumes pullups on P0}

Often if you think you understand something, the easiest way to confirm
is to make a small change, and verify that changes 'as expected'.

Also write the HEX values, as binary, or ask the Debugger to show Binary.