Say I have a stored procedure consisting of several separate SELECT, INSERT, UPDATE and DELETE statements. There is no explicit BEGIN TRANS / COMMIT TRANS / ROLLBACK TRANS logic
You must understand that a transaction is a state of the session. The session can be in an explicit transaction state because there is at least one BEGIN TRANSACTION that have been executed in the session wherever the command "BEGIN TRANSACTION" has been throwed (before entering in a routine or inside the routine code). Otherwise, the state of the session is in an implicit transaction state. You can have multiple BEGIN TRANSACTION, but only the first one change the behavior of the session... The others only increase the @@TRANCOUNT global sesion variable.
Implicit transaction state means that all SQL orders (DDL, DML and DCL comands) wil have an invisble integrated transaction scope.