I hesitated to answer because I was positive at least one of the answers was going to have some wacky interpretation.
DBCC CHECKDB does not fail when run against either master or tempdb, unless some other conditions are met. It MIGHT fail against any database, given a sufficient level of data corruption or hardware failure, but it is not true that it WILL fail against tempdb or master.
From BOL under "DBCC CHECKDB":
Checks the logical and physical integrity of all the objects in the specified database
I don't see any quibbles there about statistics. It may not refresh statistics, but it does check that they are correctly allocated.