I'm the man who did all the measurements on the above stated website, and I have to say that from the time I publish my results some things have changed. So you are better to don't read the english version of the page, and try to read the czech one instead (
http://prirodni-akvarium.cz/index.php?id=mereni), which is more accurate and up-to-date. Unfortunatelly I don't have a time to update the english version as often as the czech one. So try to use Google Translate on the czech version. What I can say is that there is surelly a difference between the PAR values 1) "outside the tank" = in the air, 2) "in the empty tank", and 2) "under water". If you measure light intensity "in the air" (outside of a tank) then you'll find out that (in accordance with physical laws) the light intensity decreases with distance ... so the further you are from light source, the less light you get. But this doesn't hold true if you measure the light in a glass tank (wheather empty or full of water). While the light intensity decreases in the tank the same way as "outside the tank", there is an increase taking place in the tank also, and this increase (due to reflections) is much higher than the decrease caused by the physical laws which applies outside the tank. So this is the reason why you measure higher values in the tank than outside the tank. I use Apogee MQ-200 PAR meter for all my measurements which is quite respected device. Also what's quite interesting is the fact, that in cube tanks the reflections are much higher that in rectangular tanks (in cube tank the light intensity can be up to 3-times higher than outside the tank, while in rectangular tank the light intensity can be only a little higher compared with the values measured outside the tank). The same applies to small vs. big tanks (small tanks = higher impact of reflections). Also the difference just above the water surface vs. just under the water surface are small => about 10 µmol PAR according to my findings. Next week I will do some further measurement with ADA Aquasky also (at least I hope so). So I'm working to expand my measurement so that they will be more and more accurate. Right now I'm testing Cree and Bridgelux LED chips => you can check some measurements here:
http://prirodni-akvarium.cz/index.php?id=led2 (I'm working on translation of this article into english right now). I hope it helps.