[spoiler]Barnabas doesn't simply accept Julia's help. In fact, far too often he manipulates her against her better judgment into helping him or coming over to his POV when Julia's POV is clearly the rational one and his is not. He does the same to Willie as well, particularly in the scene I've already referenced from Ep #560.
And as far as Julia goes, there is actually a classic and extremely telling exchange with Barnabas coming up in Ep #481:
JULIA: You always win, don't you, Barnabas?
BARNABAS: We can always checkmate each other, Julia.
JULIA: No. No. You stop me, though, though I seldom stop you.And that is a situation that isn't simply true in Ep #481 - it's true of their relationship throughout the series. In fact, one perfect and far distant storlylinewise example will occur in 1970PT with regard to Roxanne. (But then, as has often been said, in that instance it's more than clear that Barnabas doesn't think with the head on his shoulders.
Whereas Julia certainly doesn't have that problem in the situation.)[/spoiler]