Andrew:
¯     CMOS circuits require that all inputs be connected to power, ground or
¯     a signal.

I agree, but....

¯     I suspect you are actually providing a crude clock signal to the PIC with the clock
¯     input floating about at strange levels and being changed enough as you
¯     fiddle with the wiring to cause a clock signal for the program.

With an LED still connected to my clock (and the OSC1 connected to a wire that is pointing into space) I see the program execute in time with the clock LED.  When the clock is un-powered, the PIC ceases to execute.  Also, with this configuration, I am not touching the OSC1 input wire.

-Bill D.