How are the sources questionable? The only one that isn't the direct results of a peer-reviewed study is the straightdope.com one, and all he got from that was the Ganzfeld procedure. That's readily available and accurate anyway. Princeton's parapsychology department did some of the studies as well... A lot of the stuff came from Rupert Sheldrake, and he invites others to replicate the experiments. What source specifically are you talking about, and what makes the results flawed?
Ganzfield Experiment Criticisms:
"Isolation — Richard Wiseman and others argue that not all of the studies used soundproof rooms, so it is possible that when videos were playing, the experimenter (or even the receiver) could have heard it, and later given involuntary cues to the receiver during the selection process.[24] However, Dean Radin argues that ganzfeld studies which did use soundproof rooms had a number of "hits" similar to those which did not.[4][18]
Randomization — When subjects are asked to choose from a variety of selections, there is an inherent bias to choose the first selection they are shown. If the order in which they are shown the selections is randomized each time, this bias will be averaged out. The randomization procedures used in the experiment have been criticized for not randomizing satisfactorily.[25]
The psi assumption — The assumption that any statistical deviation from chance is evidence for telepathy is highly controversial, and often compared to the God of the gaps argument. Strictly speaking, a deviation from chance is only evidence that either this was a rare, statistically unlikely occurrence that happened by chance, or something was causing a deviation from chance. Flaws in the experimental design are a common cause of this, and so the assumption that it must be telepathy is fallacious. This does not rule out, however, that it could be telepathy.[26]"
A statistician must be meticulous. A single factor- meaning if ANY of the listed above has merit, it would disqualify the legitimacy of the experiment.
Especially number 3 - As I've taken my stats myself, you can never ACCEPT the null hypothesis. Rather, you can only FAIL to reject it... meaning, even if these studies are valid (which I am dubious), you can only say that telepathy is still a viable answer, not that telepathy is the answer.