Must a PI who collected data but did not contribute to its final analysis be one of the authors in the paper?
This doesn't seem to be related much to the fact that the other person is a PI. According to the question, someone collected data, and you have analyzed it. 

Unless the data was published elsewhere, you cannot cite it. So you will need to include the person who collected it as an author in order to have a source for the data. It's hard to expect otherwise, if you want to use unpublished data as the source for a paper. 

The ICMJE guidelines agree; one of their criteria for authorship is:


  Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; AND


The other person has met this point through acquisition of the data.

The most gracious thing to do would be to offer the other person a co-authorship, which will then allow them to meet the other three bullet points in the ICMJE guidelines. 

The other person can then decide whether to accept the co-authorship, or whether to take a smaller form of acknowledgment for the data collection.