In the debate around the extended mind, the special alliance that the extended thesis often has with functionalism usually plays in favor of the former, with functionalism providing support for the extended thesis. Here I want to consider this alliance in the opposite direction: does the extended thesis provide support for functionalism by promoting the need of a level of explanation that is independent of implementational (in particular neural) details? In spite of a seemingly promising line of reasoning for an affirmative answer, I show here that a commitment to the extended thesis or any version of externalism neither paves the way for a functionalist (or any other anti-reductionist) position nor is incompatible with an explanatory reductionism about the mind. I arrive to that conclusion after analyzing an argument by van Eck et al. (2006) meant to conclude the opposite, and showing why it is unsound.