> "I don't think anybody saw it coming."

I assume that this sentence means that the speaker thinks nobody saw it coming, but can't this pattern "I don't think anybody X" be took as "I think that not everybody X (but I think some X,)" in some context? 

In other words, do you always take the example sentence I quoted from [this article][1] as "I think nobody saw it coming," not as "I think not everybody saw it coming, but I believe some did at least?"


  [1]: http://www.indystar.com/story/sports/college/notre-dame/2016/11/09/irishs-mike-mcglinchey-election-dont-think-anybody-saw-coming/93554704/