If anyone wants further knowledge about effettivamente, here are some links:
Wiktionary doesn't list effectively as a translation: https://en.wiktionary.org/wiki/effettivamente
With examples of usage - the examples seem to suggest against effectively: http://it.bab.la/dizionario/italiano-inglese/effettivamente
Duolingo's own dictionary: https://www.duolingo.com/dictionary/Italian/effettivamente-adverb/84b5479d683a3b1997071f5347d1d192.
I did more research than above, but it was fruitless, so not worth sharing. If any one in the know about effettivamente, effectively and actually wishes to provide guidance for us learners, that would be good.
Meanwhile (caveat, I'm a learner, so this is guesswork) I suspect from the fact that effectively is not already accepted, that there is a nuance here that the course contributors wish to convey. If so, it could be that effettivamente (and actually) in this sentence means the reality is that they are right, whereas effectively would mean the reality is that they are not right, but it doesn't really matter because it works out the same (very roughly for both sentences).
Thanks for all the research. I see your point about the distinction between 'actually' and 'effectively', and agree with you. But it is confused by DL offering 'in effect' as a translation, and Wiktionary gives 'in effetti' as a synonym. Surely 'in effect' and 'effectively' mean the same thing? So it does look like DL is being a bit inconsistent here.
https://www.merriam-webster.com/dictionary/effectively Effectively: "...2. In effect"
http://dizionari.corriere.it/dizionario_sinonimi_contrari/E/effettivamente.shtml Effettivamente: "in effetti"