I think that is a common misunderstanding of the inverse square law, I've heard it before. People ask if they get a short throw lens if it will make the image brighter because it's closer.
The answer is NO, it's not the distance it's the size of the image which the brightness is proportional to.

I see where the confusion happens, if you have two matching projectors (with the same lens) and one is 5ft away from the screen and the other is 10ft away from the screen: then the one that is 10ft way will be twice and high and twice as wide, therefore 4x the sq feet of image surface.
The same amount of light is spread over 4x the area making it 1/4 as bright.

It's the increased area that makes it dimmer, but it's the distance that makes the area larger, thus the mistaken connection.

So lets clear that up, by taking one of those projectors and putting in a wide angle lens, one that makes the image 5ft wide from 5ft away. The other has a long throw lens that makes the image 5ft wide from 10ft away.
Now both images are 5ft wide, from the same lumen projector and ... both images are the same brightness.

We move the short throw projector back to 10ft away, and it's now got a 10ft wide image, and is 4x the area and 1/4 as bright.

so we can change distance, or the beam spread of the lens, and both things change the area of the projection. Now distance is decoupled from area, but we see that it's area that is proportional to brightness not distance.

Now just for fun in case anyone needs it lets look at the inverse sq law and how it is about Area.So far that was nice and easy with 5ft and 10ft, lets put the long throw lens back in both projectors and put one at 5ft and one at 15ft. Away from the screen.

One image is now 5ft wide and the other 15ft wide.

3x as wide.but it's also 3x as high, meaning that it's area is 9x as large, and it's brightness is 1/9th less.

5ft vs 20ft 25x difference. 

in the likely event that that was not clear check out a more detailed explanation. 
http://en.wikipedia.org/wiki/Inverse-square_law