In recent years, surface coatings or treatments have been used increasingly on paper to improve their runnability or otherwise fit them for use. Sometimes this treatment or coating (which may be undetectable to the eye and hand) has a pH that is much higher or lower than the paper it is applied to.
This makes spot tests misleading, and can lead to a lot of anguish, if the distributor or sales agent knows they are selling alkaline paper and the customer uses a pH pen that appears to tell a different story. (Printers and others who might be more concerned about surface characteristics than about permanence would not be so disturbed about the discrepancy.)
In order to learn whether a paper is really alkaline nowadays, you have to accept the alternatives described in the new ANSI standard for paper permanence, Z39.48-1992: either tear the paper to expose the inner surface, and do a spot test with a pH indicator such as chlorophenol red, or accept the manufacturer's certification that the core paper is alkaline and was made at an alkaline pH.
Every subscriber to the Alkaline Paper Advocate should have received a pH pen for spot tests with their first issue. Unfortunately, the instructions on the pen's barrel do not say anything about tearing the paper, but the instruction sheet is being revised to include it, and the next batch of pens will have revised instructions.