Thank you for this crystal clear explanation.
The datasheet is very clear too about the state of the pins at powerup.

I've tied the pin to GND with a 4.7K WPD resistor but still it would be HIGH at power-up.
I moved the PORT (setting it to 0) and TRIS (setting it to input) for this pin right at the top of my source code: it helped. Later in my code the PORT and TRIS registers are set to the right settings (my pin has to be used as output as it outputs a pulse).

Hope this helps others.