No it's definitely a transactional replication publication.
I will turn off the auto create stats - still a little confused though. The statistic was a weird name (hind_133213 or something) which I don't think is an auto stat, and the same name existed on both databases. There is no index or column called hind, and chances of it being the same name should be pretty slim. I think it was replicated across and an untrapped error occurred, which left the replication in disarray.
What is more concerning is that there were empty tables in the database. I have the articles set to delete data from tables on the snapshot page, and I assumed that this only occurred (deletion from table) when a snapshot was produced (i.e. on reinitialisation). This seems to indicate that a snapshot was performed, but I have no idea why that should have occurred. I assumed that with a transactional replication only the new/edited/deleted rows were replicated, not the whole of the table after each change.
Anyhow, have turned off the auto create stats and will see what happens. I am interested as to what impact that will have, the 2005 database is for reporting only, so I would expect it to have different statistics from the 2000 database (which is the data entry database) as the data is used in a different way.