Standing + Avoiding Machines = Athletic ?

Mario / Martin Rios are brothers who advocate for "athletic" and "functional" training over bodybuilding training, as it translates better into sports, daily life, and reduces chance of injury. The two brothers contrast pretty sharply with "hypertrophy optimalists" who are everywhere on social media right now.

Their claims are that we should avoid machines, try avoiding exercises sitting down as they require less core, and that the lack of stability is a good thing since in real-life movement is initiated by the core. He's vehemently against the Smith machine as well. An example Mario uses is that if your strong at lat-pulldowns a lot of the time they won't be strong at pull-ups, which I guess is true. However if your good at pullups, you'll know you have a strong lat-pulldown.

So, does doing exercises with more stability like chest / shoulder press machine, or smith-machine "affect athletic" ability?