But there are difficulties with that scenario, because if Hydra sent its own team - rather than a team of Hydra agents who were formally SHIELD agents, or a team combining both Hydra moles and loyal SHIELD agents -, there would be no point in sending SHIELD teams as well and/or classifying Skye as an 0-8-4.
So, that option does not seem to work.
An alternative hypothesis is that the first SHIELD team was actually a pure Hydra (but formally SHIELD) team. But that does not work, either, because in that case, the senior agent would have been Hydra, and would have had no reason to call the second team, let alone to say that the whole village died protecting the 0-8-4.
There is also the hypothesis that the first team was a mixed Hydra/SHIELD team (formally all SHIELD), and the senior agent was SHIELD, not Hydra. But when the agent called Lumley's, there was no sign of fighting within members of his team, so any Hydra members remained covert at that point. But if that is the case, who killed the villagers?
A Hydra team that got there earlier is a hypothesis, but it doesn't work in my assessment because of the reasons given above (i.e., no reason for SHIELD to be involved at all or for Skye to be classified an 0-8-4 if Hydra was going to send their own (not formally SHIELD) team).
P.S: While I enjoy speculating about fictional stories

, sometimes I just have to admit there is no answer - and that is looking increasingly probable in this case -, at least not without involving unknown third parties, or unknown motivations in known parties (e.g., maybe Lumley lied for some reason unknown to us.