I tend to agree with your hypothesis: firstly, I don't think that the strong form of the Sapir-Whorf Hypothesis holds for natural languages [0], which sets the bar pretty low for PLs. And secondly, the SWH does (seem to) hold for programming languages: the cognitive tools and abstractions reached for by users of language A can be very different from those reached for by users of language B. Lisp users, Haskell users, C users, Forth users, etc all seem to think about problems differently. It would be interesting to see some empirical work on this.
[0] Almost all post-Chomsky linguists agree with this, but there are a few that have tried to argue that you can kind of bend the strong form to make it fit some empirical results; see the color word research of Paul Kay for example -- http://www1.icsi.berkeley.edu/~kay/Kay&Kempton.1984.pdf
After all, we hear all the time that programmers in a particular environment analyze problems differently, or think of different solutions, or do or don't write certain kinds of bugs, compared to programmers in a different environment. Since strong forms of Sapir-Whorf have come in for so much criticism among linguists as applied to natural language, I'm not sure my intuition about this points in the same direction as the author's!