Eagle board editor not allowing me to place components outside area which is permitted
For EAGLE Light Edition the part needs to be placed within the 100 mm x 80 mm (4 inches x 3.2 inches). The area starts at the origin and includes 100 mm to the right on the horizontal and 80 mm up on the vertical. 

The thing is, someone can make a board in a paid version of EAGLE and place parts in a larger area. Then you can open that file, but you'll have the aforementioned limitations. So, unfortunately, you can only edit parts in the area that you're allowed unless you buy a version of EAGLE. I recommend EAGLE Hobbyist. I happen to own EAGLE Hobbyist. I'm able to edit all areas of the board that you linked to.

However.

I see that this board fits well within the limitations of the free version of EAGLE. If that's the case then the problem is you're trying to drop the part outside of the limitation. For instance, in your screenshot, you can't place things below or to the left of the small grey + in the bottom left of the picture, that's the origin. Place the part anywhere, within the aforementioned limits, above or to the right of that. The new part in your screenshot is in the illegal area.