I don't think she got the nomination because it was her turn. I think that she got the nomination despite the fact that it was her turn. Certainly very few political observers thought going into the 2016 Democratic primaries that Hillary was going to have a difficult time of it against a 75-year-old democratic socialist.
But she did get the nomination, and she was clearly the candidate whose turn it was. The Democrats just really seem to have something against going with the obvious candidate, and indeed if you look at their history, you can see why.
1956: Nominated Adlai Stevenson, candidate whose turn it was. Democrats lost.
1960: Nominated JFK, while Stevenson (who had been a sacrificial lamb in 1952 and 1956 against the overwhelmingly popular Eisenhower) was the man whose turn it was. Democrats won
1964: Sitting president nominated.
1968: Nominated Hubert Humphrey, candidate whose turn it was. Democrats lost.
1972: Nominated George McGovern, while Ed Muskie was arguably the candidate whose turn it was. Democrats lost.
1976: Nominated Jimmy Carter. I don't know if there really was a candidate whose turn it was; you could argue Sarge Shriver (who had been McGovern's running mate in 1972). Democrats won.
1980: Sitting president nominated.
1984: Nominated Walter Mondale, whose turn it was. Democrats lost.
1988: Nominated Michael Dukakis, whose turn it was. Democrats lost.
1992: Nominated Bill Clinton. You could make an argument for Sam Nunn or Mario Cuomo as being whose turn it was, but neither of them ran. Democrats won.
1996: Sitting president nominated.
2000: Nominated Al Gore, whose turn it was. Democrats lost.
2004: Nominated John Kerry, whose turn it was. Democrats lost.
2008: Nominated Barack Obama, while Hillary Clinton was clearly the candidate whose turn it was. Democrats won.
2012: Sitting president nominated.
2016: Nominated Hillary Clinton, whose turn it was. Democrats lost.
It's a small sample, but it sure looks like when the Democrats go for the candidate whose turn it is (other than sitting presidents) they lose.