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If I were a betting person, my money would go on "false." Nest building doesn't usually start until a few days before the kits (real or not) are due - some does don't do anything until just hours before they kindle. Most does don't even pull fur until just before they kindle, or just after. Fur pulling is often the sign of the end of a false pregnancy, particularly when it occurs only a couple of weeks after a known encounter with another rabbit (it doesn't even have to be a buck).
Of course, rabbits don't read the books, they just chew on them; not all does follow the typical pattern. I had one Jersey Wooly doe that started fur pulling at day 21, and continued to pull for days after the kits arrived. She wound up completely bald, except for her head and feet, and a little "Mohawk" of hair right along her spine. She was an extreme case. When she first started pulling fur so early, I thought it was false pregnancy, but the fact that she continued to do it inspired me to keep the nest box with her, which turned out to be a good thing.
With this doe, my inclination would be to keep the box with her, just in case, but not to expect anything. Every doe is different; making mental notes about this doe's behavior can help you to know what to expect from her in the future. ("normal" for some does can be pretty far out - I had one that
always fought with the buck before she'd breed, and completely ignored her nest box until just before the kits were born. She was a great mother, though . . .) Often, fur pulling on a doe that you know isn't bred can be a signal that she's at a hormonal peak, and it's a really good time to breed her.
