Matt runs Sybase instead of MySQL, you can't compare this.
MySQL optimizes count(*) queries because it keeps an extra counter in its index-files when using MyISAM Tables. The Index should be read from RAM on heavy-used tables. This kind of queries as well as MAX(indexed-column) can be answered without I/O which makes it really fast.
this sum(...,1,0) trick has to read every row from the table or just every entry in its index if its condition matches from index. so this is always slower than reading three single values with three single queries.