From Nov 2008 Books Online:
DBCC CHECKALLOC checks the allocation of all pages in the database, regardless of the type of page or type of object to which they belong. It also validates the various internal structures that are used to keep track of these pages and the relationships between them.
When you say this does not check statistics, what exactly isn't being checked? It doesn't resample the data and update statistics, but it does check the their logical and physical integrity.