Once you've got one hole you can just consider it like a sack, all the others are superfluous.
It can still be turned inside-out, but it's a little trickier to visualize. You can imagine the hole stretching until you have a pair of identical rings glued together, then it's easy to see that you can shrink the hole the same way except in the other direction. But there's no way to make it look like a sack with holes.
But there are plenty of hypothetical clothes for which this isn't true. Consider a mobius strip - like a sack, there is only one hole, but a mobius strip isn't a sack (and you can't patch it shut).
[1] I don't want to think about clothing for which this isn't the case, since it would involve the digestive tract.
http://www.zadehome.com/images/product/Racerback_Nightie_2_M...
But I think that falls into the category of "sack with a couple more holes".
I can't find a picture of it. However while this is still a "sack with a couple more holes" http://s7.kmart.com/is/image/Sears/049B018579550001?hei=500&... if you picture having that strap be wrapped around at the point of intersection it can still be unwound. However, if you form a slip knot at the intersection it can not be removed by deforming the garment.