I did want to get another English speaker to weigh in. That's weird you hear it pronounced only that way! When I watch "Gardeners' World," every single person -- with the exception of Carol Klein -- pronounces it as "a-nen-no-mee" (equal stress on all syllables)!

It's such a minor thing I try not to let it bother me, but I don't really succeed. And I suspect even TMT, whose English is otherwise impeccable, pronounces it that way, because she refused to say it for me.