Further investigation of the setup reveals
1) Programming voltage will be provided when A1's voltage is LOW.
2) If A1 is low enough, transistor Q1 will turn off and there will be 0V voltage drop across the 10K resistor and thus 13V at MCLR.
3) Short of Q1 turning off, the voltage drop across that 10K resistor will be about 4V.
4) A1's voltage measures 0.6V, whether at the terminal or on the base of Q1.
5) Above-mentioned 0.6V prevents Q1 from turning off. However, it is present even with only the high voltage (13V) connected.
6) There seems to be inadequate isolation between the two circuits, i.e. 13V circuit and 5V circuit.
Any comments, folks?