I'm vilified and don't get attacked
Solution 1:
Passing the Speech check when you approach Cottonwood Cove will allow you to get inside without hostilities, even if your faction reputation with the Legion would have otherwise prevented it. Although it seems like everyone in the Mojave can identify the Courier by sight, apparently the Legion in the Cove are more the "ask questions and be easily deceived" type.
If Boone is with you, or if you're wearing NCR armor, I don't believe you can bluff the guard outside the Cove.
This isn't mentioned in the Wikia article for Cottonwood Cove, although I experienced a similar set of events when I approached this location.