Can't use any Bugs search form for searching in any other context

From the Bugs page for a specific context (e.g. a person or project), it is not possible to do a search for bugs in another context.

<elmo> is there a bug about being able to search for bugs against a specific project? I can't seem to see that option in advanced search
...
<mpt> elmo, what page are you on where you expect to be able to see that option?
<mpt> https://bugs.launchpad.net/ubuntu ?
<elmo> mpt: actually, no, I was going the wrong way round
<elmo> mpt: I went to my page, to try and search from there
<elmo> eventually figured I have to go to the project page's bugs and advanced search from there
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<mpt> elmo, maybe that should have worked
<mpt> e.g. maybe the search field on your Bugs page should have contained "involving:elmo" by default, which you could have deleted before entering "package:name-of-package-here" then your search terms
<elmo> mpt: that'd be nice

(The "involving:" operator is part of bug 5594.)

Perhaps a more elegant way to do this would be to have two radio buttons under every search form -- "All bug reports" and "Bugs about <context>" -- where the second was selected by default.

See also bug 5447.