Re: Worryingly
A quick look at my .mozilla/plugins (in Debian 7) revealed a number of links placed to a Java plugin by Crossover Office. Despite Crossover Office supposedly being removed long ago there was a .cxoffice directory containing the library. In addition there was a .netscape/plugins directory containing similar links; the dates suggest that Crossover Office created that entire path. Wine doesn't seem to have set such links.
There was also a dead link to Java in a long removed LibreOffice 4.2 installation. Subsequent LibreOffice versions don't seem to have set a link.
With those links removed the relevant Java plugin disappeared from the browser. There's still an Iced Tea plugin but that's set as ask to activate. Iced Tea Java in installed from the Debian repository.
Of these I only expected Iced Tea. Clearly applications can casually install Java in the browser even if you don't expect it. Vigilance is needed.