Most of the time, it isn't actually the diction itself. Often she is actually pronouncing more consonants than most singers, most notably at the end of a phrase.
Where Patti's distinct style comes in is where she places the sound, sliding it forward, spreading, scooping, that bends the line of the melody so much you lose the words.
And it should be noted, there are whole performances of her where this isn't a problem at all, even with accents.
Her Lovett (both Philharmonic and Bway) and her WOMAN ON THE VERGE performances use the accent to great effect, to bring out the words even more.
Woman on the Verge - Invisible
Worst Pies (Bway)