from my point of view, you are correct, that they have taken the name of Buddha in order to promote their own thoughts and ideas. If it were really true that they revered Buddha, then his special teaching should still be present within the material studied by e.g. Krishna devotees. I recently went to have around 10 deep conversations with such devotees and I confirmed that they know next to nothing about his real teaching. While they insist they know, they repeatedly describe the essence of his teaching as "non-violence". However this is virtually nothing to do with Buddha's special teaching, and as a matter of fact, only someone who already has the extraordinarily high level to differentiate true from false and, put it into practice by never telling any untruth, would be capable of even practicing non-violence. His teaching is far more profound and constructive than the idea of non-violence. In fact, saying his teaching merely amounted to non-violence and co-opting his name, portrait, and tacit approval of their usage of his name, calling him an incarnation of the deity of their choice, while he cannot come to correct them, is nothing other than blatant and dear violence against Gautama Buddha. This is while they insist that the words in the gita from Krisha to Arjuna that it is literally impossible to kill are remotely valid. It's merely delusion in order to further avoid the truth that Buddha left. It seems narcissistic at best and murderous at worst. Buddha called himself a self-born, not an incarnation of vishnu, and his teaching wasn't non-violence, but rather, he even stated once that he was here to destroy delusions. it would make sense that, for a person like him, with massively superior wisdom, to have come and tamed all those around him in debate on such matters, who also said that he is the only one who exists between all of heaven and earth, thus superseding the deities of the current religions, would have to be co-opted by those religions. misinforming people is the only way for religious people to maintain their position of influence over others and over their own subconscious.

What saddened me even more was only the children I met in that large group of devotees were able to admit they had doubts about the Gita and were able to listen a bit.

Buddha also was extremely clear in the Lotus Sutra that even "nirvana" is not his real teaching. He states repeatedly and very unmistakably that he used the concept of nirvana as a temporary resting spot for beings who would be too arrogant or too ignorant to accept the truth if he told them as he knew they wouldn't be able to understand without much more of his cultivating them. So he lets them play with the concept of nirvana, and when he sees them cultivated, he tells them that what they thought was nirvana was no true final resting spot and that real nirvana resides with omniscience. He claimed knowledge of the true nature of reality and was very clear in his explanation of the fundamental laws and theories of existence: reincarnation and the law of cause and effect. How a good or bad thing happens. How to live well or how to become worse. Lying, for example, is not good for people. He revealed the ways from the problems to the results.
As you can see this is a far cry from such a thing as ordering people not to be violent and not explaining how they can actually accomplish it.

suppose you were to hear that real nirvana is with omniscience... you'd probably have thrown it away too. or suppose you are a Krishna devotee who calls said deity to help or take control of your life - and Buddha comes and calls you "the blind who have eyes"... the main answer for people who remain in denial is to co-opt his name and deny that you're in denial.

it rather reminds me of modern Christians believing themselves saved from sin just through faith in their own ideas without ever having met Jesus and having listened to him scold them on their wrong ideas and practices. why do we think humanity killed people like Jesus and Socrates? just because we pretend to be part of a gentle religion does not exempt us from the same tendency. Buddha in reality was very lonely when he was here in this world.

as a matter of fact, modern Buddhism as well is not the real, living teaching of Buddha anymore - most people I met interested in Buddhism are also co-opting his name. He was very clear this would happen in the Lotus Sutra. that's why he intentionally withheld the true Dharma from people until right before he died. Buddha's teaching is not to kill your consciousness and to die forever (no more rebirths). Buddha is clear that he made up that he dies or that he won't be reborn and says in fact he is reborn many times. Buddha's real, living teaching goes in the opposite way of dying forever - he taught people how to save their lives and live forever. It's obvious when you really understand what he left but what he left has been changed so much to the point that even the higher level explanations have been polluted by words of ordinary people.