Not sure about that 'tied up' comment. I believe she was pregnant at the time they were filming, yes. But there's a link from her website to another site in which, in an online print article, she said "when I heard the rest of the cast were doing the movie, I gagged." So perhaps she just didn't *want* to do it?
"There is no use trying," said Alice; "one can't believe impossible things." "I dare say you haven't had the practice," said the Queen. "When I was your age, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast." --Alice in Wonderland