Does boiling water alter the chemical properties of dishwashing liquid?
It depends rather strongly on your brand.

Soap, by itself, is unlikely to be affected by the boiling water. They're relatively stable, especially for an organic molecule. However, many of us use detergents that include enzymes that may denature in the boiling water, which is what your friend may have been referring to: A denatured enzyme is not very effective at cleaning at all. 

So, look on your bottle! If it mentions enzymes, it probably won't go over well with boiling water. If it's just soap, and, say, bleach, boil away!