Yes a person could say all those things but they need to support it with evidence.
With the independent direct voice - to suggest telepathy requires the construction of a complete personality not just information. It would be like suggesting, in the best cases, a person you had never met called you on the telephone and held a conversation with you so accurate in terms of personality, content and style as to convince you they were someone you knew and loved. One could 'say' telepathy but that would, imho, simply be using the word almost as some sort of magic charm. How on earth would that work? It doesn't make any sense (to me anyway).
To adopt that position with full materialisation would be similar to the independent direct voice but even more illogical as far as I can see. I may be wrong but I cannot recall reading even the most ardent skeptic suggesting that mediums could, using telepathy as an information source, construct a full human body (by some fraudulent means), which could move, speak and interact with the sitters, be recognised by loved ones and facilitate this encounter by telepathy. Is it conceivable - well yes, I just conceived of it. Is it likely? Personally I can't see how but then again I have read scores of reports of people's experiences with the phenomena and it doesn't fit. (* see point below)
Similar for trance in the conditions I mentioned. Telepathy cannot as far as I can see be used to explain the nature of the communication. Fraud is usually the explanation of choice for such people. In fact, I can't think of many skeptics who would accept telepathy as a fact, let alone be used to describe the phenomena I have mentioned.
Then there are the encounters with dead people that are not facilitated by mediums. That must be imagination or hallucination or simply lying. See it's easy to conjure up explanations that are superficially attractive but don't bear the weight of the experience for the person who has observed it when the full facts are examined.
In short, telepathy isn't a sensible response to such phenomena but short of the person experiencing it for themselves I can't think of a way to budge someone who insists it's all smoke, mirrors and the effect of something else (telepathy) that most skeptics probably don't accept exists, and those that do have never seriously suggested that it can be wielded in such a way.
* This also reminded me of the Super Psi explanation which you mentioned, which appears to be something that can be used to perform any of phenomena that may be demonstrated by mediums. Depending on your point of view it's a way to explain psi phenomena without the need for survival of death or a dualistic model. Is it convincing or just a desperate attempt to avoid the unacceptable alternative? I've never seen anyone demonstrate that kind of thing is even remotely possible with 'Super Psi'. Chris Carter I think disposes of it pretty well in one of his interesting books. It could be aliens using invisibility cloaks of course.
Imho there's no point in arguing with people who dogmatically assert their position when it doesn't fit the reported fact or what has been shown to be possible with telepathy. The difficulty is that unless we have experienced it ourselves, or can show them, they have a position which it is difficult to falsify. In any even what would be the point? What would one be trying to achieve?
You're right it is a stalemate. The answer is, I think, to form a personal view of the evidence and test the strength of skeptical arguments against that view, being prepared always to revise our view if the argument is strong enough. Sceptical arguments can be a good way to increase one's knowledge and refine our opinion but without incontrovertible evidence people can always find a way to stick with their original thinking if they want to. After all, the certainty of knowing we are right is very powerful and comfortable isn't it?