By recording data in a transaction and thus a block, it can be proven to any external auditor that the data has not been tampered with since a particular date.
Anyone can verify R is created with knowledge of data by verifying if Equation 4 holds, since all variables are publicly known.
An outside observer can only see r in her signature and cannot know if it is from a k generated with or without Equation 3.
If Alice does not have any bitcoin, she can ask Bob to timestamp her data into his signature.