Example 2 surely is not sabaki. But is Example 1 even Sabaki? To me this looks like a situation where Black has a shimari and White attaches, Black hanes, and now White decides where to play. White can possibly start a ko (but Black can just connect). If White does start a ko in a position where White had nothing and Black has a lot to lose, is that not making a HanamiKo rather than making sabaki? Another thought -- is there a term for playing moves inside the opponent's territory in order to get your "free" moves on the outside? Not necessarily a squeeze but something like that. This example seems more like that since it solidifies the opponent's position in exchange for some stones outside.

The example also states "White may then continue at a" but it is Black's turn. Black can simply connect to secure the corner and White has their ko on the outside.