Blackmore starts off by saying that the parapsych route away from naturalism is closed off because her own experiments failed to produce evidence. But she's demonstrably wrong here. Berger has published a fairly strong critique of her work, which failed to discuss the plethora of strong cases (references available upon request) and contains  methodological faults. See http://archived.parapsych.org/psiexplorer/blackmore_critique.htm

Blackmore has replied to Berger in an equally forceful paper. Her rejoinder contains some admittedly valid and worthy counterpoints, but she nonetheless admits the following: "in spite of Berger's numerous errors, I agree that one cannot draw conclusions about the reality of psi based on these [Blackmore's] experiments. The results are relevant to the problem of replicability in para- psychology, but as far as the reality of psi is concerned I draw only one conclusion: I don't know. [...] [Berger] has made numerous errors and has seriously misrepresented my work. Nevertheless, I am glad to be able to agree with his final conclusion—'that drawing any conclusions, positive or negative, about the reality of psi that are based on the Blackmore psi experiments must be considered unwarranted'" (See "A Critical Response to Rick Berger" at http://www.criticandokardec.com.br/blackmore.pdf)

Again, Blackmore is wrong about the issue of replicability in several areas (albeit not all, so she's not entirely wrong), but I would have to elaborate in a follow up comment to avoid making this one too long.

To avoid confusion, I don't think psi effects prove anything supernatural. Perhaps naturalism is compatible with psi effects, though we may end up having to expand our notion of "nature" and "physical" (which isn't meant to be a way of sneaking in anything beyond the physical). My point is, instead, that Blackmore is sadly being a bit dishonest here. I really like her, so it pains me to say this.