I've heard statements like this many times over the years, and it's perhaps expressed most clearly by Preacher & MacCullum (2003), which is a popular paper on stats.stackexchange.com (e.g. mentioned twice in this question thread). Preacher & MacCullum write on p20 that
PCA does not explicitly model error variance, which renders substantive interpretation of components problematic. This is a problem that was recognized over 60 years ago (Cureton, 1939; Thurstone, 1935; Wilson & Worcester, 1939; Wolfle, 1940), but misunderstandings of the significance of this basic difference between PCA and EFA still persist in the literature.
I could not find all these old papers, but the Wilson and Worcester (1939) one did now allow me to reach a clear conclusion about why failing to explicitly model error variance should make the substantive interpretation of components problematic.
Cureton, E. E. (1939). The principal compulsions of factor analysts. Harvard Educational Review, 9, 287-295.
Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift's electric factor analysis machine. Understanding statistics: Statistical issues in psychology, education, and the social sciences, 2(1), 13-43.
Thurstone, L. L. (1940). Current issues in factor analysis. Psychological Bulletin, 37(4), 189.
Wilson, E. B., & Worcester, J. (1939). Note on factor analysis. Psychometrika, 4(2), 133-148. Chicago.
Wolfle, D. (1940). Factor analysis to 1940. Psychometric Monographs.