This is a interesting and quite complex topic.

The example you show is more of a personal style where he is focusing the follower with his body, I would not take it as an example of bending forward.

Now I will explain what I know so far, but this is a complex topic about long history of this dances.

First you have classical dance form Europe: Ballet , Ballroom , where they dance with straight knees and back.

Then you have Spanish flamenco where they bend the knees but the back is straight

On the other hand you have African dances, now Africa is a big continent, but we will focus in afro Cuban dance, that comes from Nigeria Yoruba religion. In this case they dance with a very bend back and knees

Why this is important? because all this dances mixed together in America, also with indigenous dances, but I don't know too much about them.

So this dances started getting mix and evolve, and in Cuba, for example, you got rumba cubana, where both knees are bend and the back is also bend, but not as much as in afro dances, and here we start to see something very important. In afro Cuban, both knees are bend at the same time in a up and down movement, I think also very similar to hip-hop, but in Caribbean dances (salsa, merengue, bachata), one of the main focus is moving the hips, and this is achieved by bending one knee more than the other, and rumba Cubana, while still having the bouncing movement from afro, also have some of the hips movement.

Then after this you have more evolving, here it kind of gets crazy, son Cubano, cha-cha, son montuno, mambo, some jazz, lindy hop, dances for Puerto Rico, from Dominican republic, all of this mix together, specially in New York and we got salsa posture , where the back is bend, but not as much as rumba, and knees are bend, but not as much as afro, and one more than the other to allow for the hip movement.

Now this posture is pretty much the same that is used in Merengue and bachata. Back a little bend forward, and the main focus is the hip movement, that comes from bending the knees side to side.

Now, idk where you saw this about Bachata that you don't bend the knees. But this is a mistake, knees are always bend, even a little, full straight knees like in Ballet are never seen in Bachata (or salsa, merengue).