Can you give me an example that would be relevant here?

I think you're both right. There are side channel attacks against remote hosts (timing-based padding oracle attacks agains TLS come to mind). But for the case of PGP, which is mostly for encryption at-rest, attacks like this don't seem as relevant. I say seem as relevant, because crypto attacks can be surprising :)

Here's a timing side channel attack in JavaScript that implements navigator.hardwareConcurrency: http://wg.oftn.org/projects/core-estimator/demo/

How about BEAST or CRIME?

BEAST is a design bug, insecure use of CBC mode. CRIME is a side channel attack, but the side channel that leaks information (compressed cleartext size) is not related to the language used, but again to the design of the algorithm.

The basic idea is that implementation-related side-channel attacks, such as timing and power draw, are very hard to exploit remotely. I guess you could write a JavaScript implementation of AES that is so bad that key-dependent multimillisecond jitter can be measured remotely. But it's almost impossible to do it by mistake.

The real problems of JavaScript are it's highly malleable runtime that offers no guarantees, everything is writable. So you need to improve browser support before you can write JavaScript crypto, that's why this is a great project: Google has the ability to change Chrome into a secure end-to-end platform, should they want that.

Maybe power draw is hard to exploit remotely, but Remote Timing Attacks are Practical (Brumley & Boneh, Stanford, 2003): http://crypto.stanford.edu/~dabo/papers/ssl-timing.pdf