Assuming you were taking the lane, when she said she was giving you ROW, you should have replied that the right way to do that was to move in behind you, the cyclist, and wait until you go by before making her turn. If you were in the bike lane, though, she kind of was right; a motor vehicle is supposed to yield to cyclists in the bike lane. If it was a non-bike lane shoulder, she's still right to make sure the shoulder is clear before she moves into it.
If you were in a shoulder/bike lane, though, it simply points to one of the problems with that type of infrastructure: It is not always clear who has the ROW. If both people yield ROW to the other person, you end up with a situation like you experienced. If neither one yields, we'd be reading a linked article about you right now.
Assuming you were taking the lane, I think she was technically right, but you did the wise thing by waiting because that is the type of situation where most of the time the driver will ignore the cyclist.
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I stop for people / whose right of way I honor / but not for no one.
Originally Posted by
bragi 
"However, it's never a good idea to overgeneralize."