I actually built a Chrome extension that does exactly this, and for all web pages. The source code is on GitHub.
I find three bugs with Trello's approach, which I know because I've faced them myself :)
The copy doesn't work in these scenarios:
I solved #1 by always having a hidden span, rather than creating one when user hits Ctrl/Cmd.
I solved #2 by temporarily clearing the zero-length selection, saving the caret position, doing the copy and restoring the caret position.
I haven't found a fix for #3 yet :) (For information, check the open issue in my GitHub project).