Yes, in Australia some people got quite peeved (or pretended to be) in the nineties when the governing progressive party decided to change leaders. Let’s name names, if that’s permissible – I refer to the caucus of the Rudd Labor Government, which decided to call a spill of leadership positions. After this Julia Gillard replaced Kevin Rudd as party leader, and therefore Prime Minister.
The Opposition Leader at the time, Tony Abbott, made a great fuss about how the Australian people had been unable to vote directly for whomever they would like as PM. Abbott claimed that Kevin Rudd deserved to be treated with more respect, not just cast aside, etc. Abbott knew well, however, that PMs are not directly elected. As has been explained much better than I can: after a general election, the party (or several parties in coalition) who can command a working majority of the House of Representatives get/s to form the government. The head of this party or coalition thus becomes the PM. (Of course this person also has a seat in the House of Reps.)
My point being – people only get to vote directly for their local member of parliament. They don’t get to vote directly for the PM. (OK, they get to vote for the representatives of their state in the Senate as well, but we won’t go there.) This fact illustrates one of the main differences between a parliamentary and a presidential system. Of course Abbott, as an experienced parliamentarian, would have been well aware of this. Some would dismiss his protests therefore as hypocritical mischief-making. As the line from ‘House of Cards’ goes, “You might very well think that, but I couldn’t possibly comment”.