In particular, their statement seems to claim that it's almost entirely due to their view that the U.S. might choose not to pay back its bonds, not that it couldn't; when explaining what's changed since previous assessments, their statement mainly focuses on the political will to service debt.
That's wrong, the GDP and expected GDP is a big part of the rating-- known as the "capacity to repay".
Doesn't the phrase "capacity to repay" make it clear that GDP matters only to the extent that it is a risk factor?
Listen to the Planet Money podcast. Lots of factors are considered, including political ones.