Skipping chunk X of Y.Z because MySQL chose no index instead of the word_sid_typeindex
The message is both expected and disturbing.
WHY EXPECTED ?
I don't find this message disturbing at all. I would expect pt-table-checksum to bypass chunks since there is no defined uniqueness. Granted, InnoDB will create a row-based index called gen_clust_index when there is no PRIMARY KEY or UNIQUE INDEX. So, chunks read from the table have no rhyme or reason to its order other than order of insertion.
WHY DISTURBING ?
Since you have a replication tag on the question, now this becomes disturbing.
When you have many writes on a master, the slave may write rows in a different order than the master. If the search_index table had a PRIMARY KEY or a UNIQUE INDEX, that would stabilize checksum evaluation. Unfortunately, that cannot be said in the case of a table that has an internally generated index (gen_clust_index) as the only form of uniqueness with an InnoDB table ON BOTH MASTER AND SLAVE.
SOLUTION

Define a PRIMARY KEY for search indexon the Master.
mysqldump search_index from the Master and load it into the Slave