You're right!

Yes, this reasoning is almost certainly fallacious. The odds of one in 50 million were calculated using the simplified multiplication rule, which only applies if the two events are independent. But giving birth to triplets the second time may well not be independent of giving birth to triplets the first time; the woman may have a biological predisposition for multiple births. In that case, the probability of the second set of triplets--the probability of a woman giving birth to triplets given that she has already had triplets--may be considerably greater than 1/7000. The chance of having two sets of triplets is obtained by multiplying this probability by the chance of having the first set of triplets (1/7000). This chance is still very small, but it may be nowhere near as small as reported.