That's only true if you run in Implicit Transaction Mode (SET IMPLICIT_TRANSACTIONS ON).

Otherwise you have to execute a BEGIN TRAN to start a transaction.

There is no transaction, according to the question. You are coming into the trigger without being in the context of a transaction. In other words, there was no "begin transaction" executed...

Please read my post. According to the text of the question, we aren't running in a transaction. No transaction = no rollback.

The question didn't state that the statement that caused the trigger to fire was running inside a transaction.