The loophole relates to individuals who do not declare a name change to police. If they tell the police then DBS would be updated, but if the person changes their name by deed poll, does not tell police, and then applies for a DBS check with the new name, it won't show up. It also assumes that the employer does not ask for any id like a passport or driving licence, to verify the persons name.
So in reality the numbers of people doing this are very small and the risks are very low, but the MP simply assumes that all SO are trying to do this, so that they can reoffend. Sarah Champion claims that 16,000 SO have breached their notification requirements and she just assumes that this means they have all changed their names and are actively trying to reoffend.