Your understanding is correct; the list number (known in CSS as a list marker) should exist outside the p, not inside it. That should be the case even if you specify list-style-position: inside because like you said, you're applying overflow to the p, not the li.
Every list item in general creates a principal block box for its children, and another box for the marker to reside in. The child elements should all be rendered within the principal block box. From the CSS2.1 spec:
CSS 2.1 offers basic visual formatting of lists. An element with 'display: list-item' generates a principal block box for the element's content and, depending on the values of 'list-style-type' and 'list-style-image', possibly also a marker box as a visual indication that the element is a list item.
A slightly more detailed explanation of principal block boxes can be found here.
In your case, each li creates a principal block box and a marker box. The p.overflow-hidden elements should reside in the principal block box and not affect the marker. Here's a crude ASCII art diagram to show what I mean:
list
marker li principal block box
+-----+ +----------------------------+
| | |+--------------------------+|
| ? | || Moo (p block box) ||
| | |+--------------------------+|
+-----+ +----------------------------+
Now, the spec seems vague about the positioning of the marker box itself, but it does say that the marker box is separate from the principal block box when list-style-position is outside. It does seem to imply also that a browser could get away with placing the marker box in the principal block box so long as the marker content actually resides by itself in that marker box (which, incidentally, cannot be targeted with CSS as yet).
But Safari and Chrome appear to be doing something very different altogether: they seem to be putting the marker box not only within the principal box, but within the first child of the principal block box. That's why it gets cut off when positioned outside the p block box: because the rendering engine sees it as part of the p content, sees that it's out of its horizontal bounds, and cuts it off. (I suspect it gets clipped with overflow-y: hidden as well because it's positioned beyond the left edge, which shouldn't normally happen in LTR mode, but that's just a wild guess.)
When you add list-style-position: inside to the li, other browsers correctly shift the p block box beneath the marker, but Safari and Chrome simply move the marker into the p box. Although CSS2.1 says that it doesn't define the exact position of a list marker with respect to the list item's principal block box, it does say this about list-style-position: inside:
inside
The marker box is placed as the first inline box in the principal block box, before the element's content and before any :before pseudo-elements.
That's clearly not what Safari and Chrome are doing with the marker box.
Again, the spec is (rather deliberately) not 100% clear about this, but I would certainly not expect the list marker to be a child of, or be affected by, any of the li's child elements the way it appears to in Safari and Chrome. I'm pretty sure this is incorrect behavior, i.e. a bug.
