Just to start off - i'm agnostic so i don't know

- but i tend to want to jump in to defend uncertainty in the face of absolute-sounding claims. Most of the actual science that backs up the certainty isn't actually as certain as the concepts based on it become (the whole idea and nature of knowledge is contested in epistemiology). Most science becomes metaphor for most people, and we often extend the metaphor without justification from the actual reality (and often need a totally new metaphor (the territory not the map and all that).
Your characterisation of a medium is a little ungenerous - you're basically describing a seaside fortune teller (who do probably make up the bulk of the profession), but mediums/psychics can be a lot more sophisticated than 'you'll meet a tall dark stranger' (most 'proper' mediums/psychis don't do that anyway, more talk about you now). Seems like a straw man really (like arguing against religion but only dealing with the bible/quran).
Mediums and psychic activity have been with humanity from the start (judging by hunter gatherers) - at the very least they have an evolutionary function along with the rest of shamanic tradtions (and maybe we should wait till we truly understand that social function before writing them off inherently).
I'm totally prepared to accept the likelihood that psychics/mediums get their stuff (what there is of it) from 'natural' means (it's the most obvious answer after all), but i can also
entertain the possibility that underneath it all is a tenuous access to some as yet scientifically-undiscovered 'collective unconsciousness' (or some such hippy/hindu concept), and that the best way to get access to this is through our inuition (meaning it will always come across as flaky). There's enough leeway in physics (and not just for the new age version) for me not to dismiss it completely; plenty for some new einstein to turn what we know on it's head (it's sort of inevitable that the next big move will do this due to the contradictory things that will need to be tied up).
I also entertain this idea partly due to 'empirical' subjective experience (ie ego death) suggestive of this sort of reality (magical thinking probably, and no help/relevance to anyone else). My intellect wants to be reductionist and leave it at that, but i've learned not to trust my intellect totally when it comes to existential questions (because it's biased towards materialism, and it's own future pleasure (bias is bias)). My intellect usually gets the upper hand, and i come down on the side of the genuine medium 'hits' being the marvel of intution (not that much of a mystery in itself, just in the mechanism). When the medium is genuine (consciously), i still can see possible value in someone who may be more in touch than most with their intuitional powers (same as a musician or snooker player (or medium as emotional Sherlock)).
Saying all that, i'd go with your Barnum version in nearly all actual professional mediums (and probably the 'good' ones do barnum stuff when the juices aint flowing too (i see how easy i'm making your arguments

).
How can you say it wasn't a strange brain function that caused that feeling / false memory when everything you think, feel and remember is a brain function.. it can be impossible to distinguish between the two..
Well it's about the linearity of the memory, and multiple sequential recalls before the actual event - but we can't be certain about anything we perceive ultimately (descartes problem) - i'm as sure as about anything else i know though (which isn't that sure i'm sure (or am i?)). I don't want to go into the details too much but it was pretty vague anyway (i didn't write down any lottery numbers or take a photo of a clock) - it was visual memories of a particular scenario/mix of people seen at a certain viewpoint (and me being on drugs won't help my credibility here) - this is more subjective empiricism for me only i guess. [/copout]
I'm totally willing to accept the probability that there was no real information sent from the future to the past (again most obvious), but i can definitely entertain the idea that there was somehow (again based on how i perceived time to work when in ego death states - no currency with a scientist, but suggestive to me, being such a 'real' experience; but also because it doesn't really clash too much with my reading of physics (given a (hindu) assumption or two)).
As far as death apparitions - it wouldn't matter if it was 'made up' she told several people about the vision before the information about the death arrived, both times. And she didn't randomly go around saying she'd had visions of relatives any other times. This has also been the case for numerous examples in the 'literature' - this is written off as anecdotal evidence by most 'science' because it can't be repeated/tested (ethical problems there), which is effectively saying thousands of people are lying - i 'know' it's not the case in at least two instances, so assume it could be true in at least some of the others - this seems more scientific to me (if i accept truth from another human i know well (science would have trouble here)).
If this was the reality (ie telepathy), it may need other science to change to account for the discrepancy (though i'm not sure it does (chuck in entangled particles or a string theory dimension). I'm not really convinced with the approach that says: 'because science says it can't be, it can't be' (it's circular logic) - if it is, it is (it's still a big if, but an if nonetheless, and one science will have to answer if it gets smaller (that's another big if ('if off!')).
I think we have problems in our culture with the over-reductionist materialist and behaviourist philosophy which dominated our science in the 20th century (and was bloody useful in many ways (deadly in others (especially to dogs and pigeons)); it often can't accept anything that can't be measured a certain way (like internal thought landscapes) - and it just pretends they don't exist/matter. Quantum physics worked it's way through our philosophy in the meantime, so we seem to be growing out of this simplistic reductionism/materialism now. In terms of ambiguity, the new and important meta-science of complexity can't even agree how to define or measure complexity itself - this doesn't make it bad science, it just means there are even more complex concepts to understand than the ones we've come to accept in the current paradigm are the mechanisms of reality.