No one really knows what the Buddha taught. All we have from close to his time are the suttas, which give no detailed methods of how to enter jhana. Modern teachers give much more comprehensive instructions (as does the Visuddhimagga, of course). What they teach is techniques that they have developed, they don't just "teach the suttas". Clearly they all genuinely believe that the techniques are based on suttas, but they are also influenced by what they learned from their teachers, and their own experience. Quite rightly, in my opinion. It seems clear from the suttas that the Buddha and others gave much more detailed instructions than those preserved in the suttas. Just read the start of MN 118: https://suttacentral.net/en/mn118. The Buddha's discourse is to monks who have had several months of intensive instruction.
[In fact, I have heard some teachers theorise that the suttas are deliberately vague, so that teachers can adapt techniques to suit their students. If they were too specific teachers would have much less scope to personalise their instructions.]
Now, Ajahn Brahm and others teach a deep VM-style jhana, which one needs to emerge from to do insight. He, and others, claim that this is what is described in the suttas. If teachers like him are correct then the VM jhana is authentically what the Buddha taught and the lighter "sutta jhana" style, where one can do insight within the jhana is not authentically what the Buddha taught.
On the other hand, as I said above, perhaps they are all correct, and the two different styles are both effective.