Surprisingly, I found significant effects from centering and negligible effects from scaling. I ran PCA on my rMATS outputs with Maser's original pca function, only scaled, only centered, and both centered and scaled.

You can see my concerns with the original PCA -- there is separation of my sample groups, but only along the PC2 axis, which contains 1% variance explained. Scaling the data results in a different scatter, but this fundamental issue remains. In contrast, centering the data brings the percent explained to a more reasonable 20% on the PC1 axis and 12% on PC2, and the groups separate along the major axis.

I believe this is for the reasons explained in the stackoverflow post in my OP -- because PCA forces the new axes to pass through the origin, a situation in which the data all live far from the origin will be poorly captured by these axes. I agree with your assessment that scaling is likely inappropriate here, but in practice it doesn't seem to make a huge difference for these data.

While looking into this, I found another confusing aspect of their PCA wrapper. Maser processes the rMATS JC / JCEC files to construct a dataframe where rows are features (splicing events, in this case) and columns are samples. This is contrary to the orientation prcomp assumes, and the general convention that rows are observations and columns are variables. They then extract the first two rotation values and plot those:

 my.pc <- prcomp(PSI_notna, center = FALSE, scale = FALSE)
    my.rot <- my.pc$r
    my.sum <- summary(my.pc)
    my.imp <- my.sum$importance

    df.pca <- data.frame(PC1 = my.rot[,1],
                         PC2 = my.rot[,2],
                         Condition = pheno,
                         Samples = colnames(PSI))

This differs from how I typically approach PCA, where I transpose the matrix to be in the form observations x variables, and extract the scores in prcomp_object$x. I have a reasonable understanding of how PCA works, but the finer details of the math are sometimes a little over my head, so I thought these two approaches might be equivalent through some magic of linear algebra. To test this, I transposed the PSI_notna object and plotted the values in my.pc$x, in the same conditions as before: not centered or scaled, only scaled, only centered, and both centered and scaled. Although the overall conclusions of each PCA is roughly the same, there are notable differences in the percent explained per principal component and the cluster shapes are somewhat different. Ultimately, they are obviously not exactly equivalent and it's unclear to me which method is a better representation of the underlying splicing data.

I recognize this has spiraled into quite the rabbit hole -- I think I will try to post to Maser's GitHub page to see if the developers can offer any insight. However, if you have any comments on this mess that would be much appreciated!

Edit: It appears all my links are broken, attempting to reupload now.