Well the article near the end says that the data for the experiment was 1.8 PB. I am not sure what the answer is, but given a mouse brain is significantly smaller than a human brain I would say Wolfram Alpha and Wikipedia are wrong.
I think you can store very efficiently. A neuron or synapse has a huge error rate. So, saving parameters of the synapse as 4 byte floating point number could be overkill. Connection information could be also reduced significantly by an intelligent sorting. E. g. you don't have to store the source index and neurons connect probably more to their neighbors then to neurons far away. Therefore I am wondering, what must be saved in 24 byte. Well, we will know, when we try it some day. At the moment it's just speculation.