Why can my Macbook play sound in Windows but not OS X?

Awhile back, a pair of headphones I owned broke off inside of the headphone slot on my Mid-2012 13" MacBook Pro. I followed some instructions suggested by people online which involved using a bit of superglue with a toothpick to get the stuck piece out of the port. Unfortunately this didn't work, and I'm now stuck with the piece of headphone in my MacBook.

Naturally, OS X will not play any sound. When trying to adjust the volume I am presented with the "system problem" icon. (A speaker with an X under it, or something similar). Basically I'm assuming it's detecting an issue with the audio port. So in OS X I'm left with no sound unless I use Bluetooth headphones.

Today, I installed Windows 8.1 using Bootcamp. After installing the Bootcamp Support Software, I was surprised to hear that I could play sound through my MacBook's speakers. I have looked online in the past trying to find a way to override the headphone port in OS X. The general consensus seems to be that it's simply not possible, because the speakers are disabled on a hardware level by the piece of headphone. Obviously this is not true, since Windows is able to play sound.

Any ideas as to why this might be, or how I can actually go about bypassing the broken headphone port? I really appreciate any help that's provided. Thank you!