His thought process is correct, but his "pen on the Moon" model is missing vital element (that Moon is in free fall/orbiting Earth).

If Moon was hanging on a stick connected to Earth (instead of orbiting Earth) and Earth gravity forces on a pen were stronger than Moon's gravity forces, then pen would fall in Earth.

Of course you and I know that there are no such strong materials for that Earth-Moon stick, but that's yet another level of complexity that most people don't have to know about.

>If Moon was hanging on a stick connected to Earth (instead of orbiting Earth) and Earth gravity forces on a pen were stronger than Moon's gravity forces, then pen would fall in Earth.

Technically that's true, but it would require a completely different scenario. Earth's gravity is miniscule at that altitude. For the moon to have a weaker force it would have to be so small that it would likely not even qualify as a moon any more.

Well, you are ignoring tides, I'm not. I say that theoretically, you could be at the Roche Limit, and then the pen would stay still. Hypothetical, yet real. So thank you very much but yeah, the thought process stand correct.

http://en.wikipedia.org/wiki/Roche_limit

You can disagree all you want, it's not because things would just fall towards the moon in practice that it's impossible that the pen stand still.

It's funny how quickly that simple "Pen on the Moon" question can be turned from novice level into physics expert level.

"Please select all possible conditions under which pen on the Moon would not fall on the ground".

Tides are purely about relative differences in gravity between positions, though, not about differences in pull between two bodies. You can still be at a point where the Earth's gravity is greater than the Moon's while on the surface of the Moon without anything floating away and while comfortably outside the Roche limit. In fact, such a situation must necessarily exist outside the Roche limit for any body.