I'm guessing you've already made up your mind that you don't agree with me. But I've learned that it's important to defer belief and judgement until after having made a confirmation. So I'll answer as if you might be interested in a sincere discussion.
> The fundamental flaw -- well, at least a fundamental flaw, its not the only one -- in this argument is that it is about "teachings from a real enlightened being" but provides no justification for applying that to "helpful teachings for enlightening yourself."
That's incorrect. What you're missing is the fact that only an enlightened being knows how to make others be enlightened and only an enlightened being can give a teaching which can be practiced in order to obtain enlightenment.
Let's say you want to learn how to fix cars… how can you learn such a thing? There are only two possible sources of the necessary information. One of them is much faster: learn from mechanics. The second one is not usually possible for ordinary people to undergo: learn from the world. In both cases, you'll be looking at the principle and problems concerning cars.
Is it possible to learn how to fix cars from people who /only/ like cars but do not know anything about them? No. The best they can do is encourage you to find someone who really does know about how cars work and what kinds of problems and causes of problems they have. But encouragement from those who do not know anything is not an essential cause for enlightening oneself. If it were, wouldn't we have more than just one or two enlightened masters in our history? Please note my usage of the term, "cause".
To me, it's quite clear that people hear what they want. There were different types of people that had interest in Buddha while he was alive, but few of them were genuinely interested in his teaching, itself. Most people had their own, individual aims for associating with him, like curing their diseases or becoming wealthier.
You suppose that those who adhere to religions might know perhaps a small percentage about enlightenment. But if they did, they would be able to tell me what the basic teaching of the enlightened being is. That's like learning the number 1 when you start learning math. But the reality is that the only answers they can give are those they read in books written by others who are not enlightened. It's hard for you to believe me unless you travel with me and meet people. Unfortunately, if you have no intention to confirm the veracity of my words, I don't think you'll be interested in judging those cases with your own eyes either.
> But this warning has been transmitted -- through religions. And clearly this warning is a teaching that must be viewed as useful for enlightenment.
Have you ever heard of the telephone game? If not, have you ever tried to make photocopies of a photocopy? The fidelity of the signal degrades due to the inclusion of noise.
The level of any monks and religious adherents has not been high enough to preserve the quality of truth which was in the teaching of the real enlightened being. As a matter of fact, most of the teachings have been completely changed, and intentionally so.
In reality, spiritual teachings are rather like food for the consciousness. A fresh apple is quite nourishing, no? (Well, it used to be, a hundred years ago!) But if the apple goes bad, to eat it would be quite bad for you. Like eating a poisonous substance. Similarly, learning and practicing the deteriorated teachings will damage your consciousness. Perhaps if you've got quite a strong will, it will take up to a year. But those of weaker will fall into danger much more quickly upon contact.
So the problem is not that a person of sound spirit can't recognize that a rotten apple probably used to be a fresh apple and can then have a fair opportunity to judge whether or not they want to eat it. The problem is that a person of sound spirit can be harmed into losing their own consciousness through contact with religious teachings and they are not informed that such things are even bad for them. If you have a connection with religious teachings that claim to be about enlightenment, it is a direct cause to damage your ability to see and transmit the truth. They make you go in the exact opposite way of enlightening yourself and only generate more bad 'karma', rather than diminishing the influence of that karma. But it is absolutely imperative to be able to stop your karma in order to achieve an enlightenment, because you cannot enter samadhi if your karma can act. Its habit is to control you. Just because you do not want to have bad karma doesn't mean that it will disappear. Karma can only be suppressed by correctly learning and making yourself aware of 'what is' at all times. It cannot be suppressed by an escape into fantasy, nor by making attempts not to think about anything, regardless of how temporarily peaceful you feel after having done so. It constitutes an intentional lie on the part of monks that they leave out the result of practicing meditation when they borrow Buddha's name and teach meditation to others. Suppose that a living Buddha came to the world? Those who would be the most afraid of him are the monks. But they're comfortable with a Buddha's statue within their temple because a dead Buddha doesn't speak, and cannot make any critique of their behavior. He just smiles at them. This only reinforces and is interpreted of encouragement of their hypocrisy.
I mention modern Buddhism as an example. I hope that you can catch my meaning through the example, so that, suppose you're really interested, you can apply it to other cases which you think may exist in the world and check for yourself whether they do or do not have the same fundamental kind of problems.
> A stronger form of this -- that the things that must be understood for enlightenment cannot be properly transmitted -- is also a religious teaching. (see, e.g., the opening of the Tao Te Ching.)
I'm sorry to say that I can't verify whether Lao-tzu actually said or meant that. I would need his exact words, or closer to them, in order to check. But to tell you the truth, it's not the case that the things for understanding enlightenment can't be properly transmitted, as you have suggested.
It's quite simple for me to do it. I can prove it anytime, on the spot. However, even if I tell you the truth or teachings about enlightenment right here, can you understand them? Only a truthful person can recognize and understand the truth. Those who are untruthful don't want the truth revealed.
Have you heard of Lao-tzu's explanation on the three levels of people? He said that their level of cultivation of virtue can be seen through how they react when they hear the truth. Only those of a high level of cultivation of virtue react with delight when they hear the truth and try quite a lot to put it to practice. Those of the middle level seem to understand, but as a result, they don't really apply it. Meanwhile, those of low level can only ridicule the truth.