Only a very thin surface layer of the water can radiate since as you correctly point out IR doesn't penetrate through water. (joannenova.com.au)
The sun heats the uppermost few meters; this has to find its way to the actual very thin surface layer to be lost. (realclimate.org)
It is one thing to say that IR is absorbed in a very thin surface layer (which he did not say), quite another to say that surface tension has anything to do with it and even then, it is incorrect to say that none of that heat is conducted downward. (wattsupwiththat.com)