Confidence Interval for R-square: R2.exe (Steiger&Fouladi) vs Bootstrapping
It seems to me that the discrepancies you're finding between the parametric and non-parametric CIs around R^2 is more an issue of the data that you are examining rather than a statistical problem. As you know, the bootstrap technique attempts to use emprirical rather than theoretical sampling distributions as a basis for drawing inferences about population parameters. I doubt that there are that many processes that can be adequately described with only 15 cases, except maybe in the most stringent experimental setting. The greater width of the bootstrap CI seems to be reflecting this and although the parametric approach seems to be giving more 'solid' results, I would treat its estimates with circumspection nonetheless. From my own work, I've found that for larger samples and with data that are reasonably well distributed, the results of the two procedures are quite similar. The situations where the methods differ are usually when non-normality, restricted range effects, and small sample sizes are too influential. Thus, I'd recommend keeping the bootstrapped CIs as is and discussing reasons why the results might diverge, and what the nature of their discrepancy might be related to. It's not a clear-cut answer, but it does give students experience with another method for determining the validity of their results rather than just accepting the parametric solution prima facie.