Does this perhaps match your experience? I.e. if for instance you have a
folder Desktop/testing, and in it a file ab.tex, and then another
folder Desktop/testing2 and a file ab.tex there, do you still see the
problem?

Yep, completely unchanged. (There were no spaces in my original test cases, but I checked "parallel" directories with no spaces in the complete paths just to be sure.)

Please pardon any repetition, but maybe it can help us get to the bottom of this: it looks to me like the root of the problem I'm seeing is in the "check_open" command, the output of which doesn't seem to depend on the location of the pdf file, but only its name. That is, consider the following sequence...

[the file "fred.pdf" from "~/Desktop/testing" is open in TeXShop; it's the only thing open in TeXShop]

% cd Desktop/testing
% /Applications/TextMate.app/Contents/SharedSupport/Bundles/Latex.tmbundle/Support/bin/check_open TeXShop fred.pdf
%

[That is, it correctly reports that the file is open. Now just change dir and see if it thinks the other pdf file is open too...]

% cd ../testing2
% /Applications/TextMate.app/Contents/SharedSupport/Bundles/Latex.tmbundle/Support/bin/check_open TeXShop fred.pdf
%

[Here's where I think the problem lies: check_open is again reporting that "fred.pdf" is open, but I'm betting that the command above should be referring to the "fred.pdf" in "testing2", not that from "testing".]

In the command "runViewer" this causes control to pass to the refreshViewer command instead of invoking the "open -a ........." command that's required.

Does this make any sense?

Cheers,
Paul