In one definition. In another it simply says that "conspiracy" is "the act of conspiring" and one of the definitions of "conspire" is:
to act in harmony toward a common end
https://www.merriam-webster.com/dictionary/conspire
That said, I don't think there's much question that the more common-place, colloquial definition includes the "secret" and probably "unlawful" aspects. But somebody who uses these terms in the other sense isn't necessarily wrong.