Yeah, I don't crouch unless I'm pretty sure that the dog isn't going to respond in such a way that I need to back up quickly. That's another area where I consider owner presence- I tend to be more wary of nervous dogs with owners vs alone, and afford those dogs more respect in the form of space because nervous dogs with backup (owner) or on leash (no option to flee) IME tend to be more apt to behave defensively vs just avoiding. And I think the slow motion in that video does an excellent job of showing how much slower humans are than dogs- the handler was right there, and still corrected/pulled the dog back well after he was done biting the reporter.
When I crouch, I usually end up crouching sort of parallel to/at slight angle to the dog because it tends to make nervous dogs feel better and it's harder for crazy happy dogs to knock me onto my butt. This also naturally orients my gaze away from them, and makes their chest/shoulder readily available for scratching without needing to reach over/around their head. Honestly, when I think about it, I rarely do standing petting head on, either. My starting point for petting/touching most dogs is the chest or shoulder (depending on their orientation to me), then I'll work my way up for an ear scratch if they seem amenable, and so on. Usually just one hand (except for crazy happys, where I feel like I could have 8 hands and it still not be enough! for them it's usually one hand to keep them off my person, and the other to pet

), and the top of the head only if they present that part.
I do think crouching is preferable to bending at the waist to pet a smaller dog, as crouching makes you smaller in general, and when you bend, your upper body tends to loom over most dogs, which is a definite negative for many.
One more thing, while it's important to always ask before petting, don't take the owner's answer as gospel. Some of the scariest encounters I've seen have been preceded by owners saying, "He's fine!", and followed by owners scratching head saying, "Gosh, he's never done that before...?". In several of these cases that I've seen, the dog has looked sketchy to me from the start of the interaction, and I've been more surprised by the owner giving the go ahead than by the dog's reaction. Yes, ask, and if the owner says no, that's it (there's probably a reason!). But even if they say you're good, you still should use your own discretion to determine if/how to proceed.
In the case with the dog in your OP, I would probably have engaged the owner in small talk while the dog was apparently distracted. Then, if the dog turned his attention to you, you could engage if he looked amenable. Either way, it sounds like things turned out well, and you made a new buddy
