First, there's no perfect reflector nor absorber. In fact - even Aluminium does absorb some radiation (by which it gets heated, can be noticed at incident high frequency radiation). One more thing is that aluminium foils are designed in a way to reflect light.
Here's the Wiki article quote...
Aluminium foil has a shiny side and a matte side. The shiny side is produced when the aluminium is rolled during the final pass. It is difficult to produce rollers with a gap fine enough to cope with the foil gauge, therefore, for the final pass, two sheets are rolled at the same time, doubling the thickness of the gauge at entry to the rollers. When the sheets are later separated, the inside surface is dull, and the outside surface is shiny. This difference in the finish has led to the perception that favouring a side has an effect when cooking. While many believe that the different properties keep heat out when wrapped with the shiny finish facing out, and keep heat in with the shiny finish facing inwards, the actual difference is imperceptible without instrumentation. The reflectivity of bright aluminium foil is 88% while dull embossed foil is about 80%.
The shiny and not-shiny surfaces are totally a favor of production technology (credit goes to the rollers). Now, to the "why" question.
As a physics parameter, we use reflectivity to address the shininess. As we can see, the reflectivity is quite high for the bright surface, compared to dull one. The unreflected light (as you say) can go anywhere. It can go inside the aluminium foil (i.e) it's absorbed and hence the 12% & 20% loss...
Response to comment (based on edit): That's a nice strange idea. With some perfection (I mean, there should be very less allowance of any sorta radiation inside), the room will be relatively cooler. But, in reality (where we can't expect idealistic things), there will always be some radiation inside. But, it keeps the room warmer compared to the outside. But, always be careful when playing with such things because, any sort of harmful radiation (if any- what about a heater or even an electric iron?) inside the room will be reflected back to you by the matte side - which can be very harmful...