Why can we Print Colors my profile says are out of gamut?

Technically speaking, if the colors are truly out of gamut, then you would not be able to print them.
It would be good if you could give us more information about what is telling you that the colors are out of gamut. Are you going by the gamut warning in Photoshop, or is this some feature of your RIP (which one), or are you using a gamut viewer like ColorThink?

If you’re looking to get good color matches with saturated colors, its generally recommended to use relative colorimetric for printing. That will give you more saturation than perceptual.

As we discovered in this Tips and Tricks video, it is possible for a profile to not give you all the saturation a printer is capable of - but a good profiling engine like i1Profiler should get you almost everything that is printable.