Absolutely right. Well spotted.
The offences in the UK are almost identical.
As mentioned by
@bobthedug, whilst the 'powers' are there, to enter without a warrant in the UK, it is usually confined to 'hot pursuit" and to save life.
As
@bobthedug says, he used it once in 30 years; I used it never in 30 years - it is a rare thing.
I think the OP's point was "Do we as FAC/SGC holders have less rights that those that do not hold FAC/SGCs?"
The answer is no.
I think the issue arrises from the standard Police letter that asks you to "facilitate' entry to conduct a security inspection without recourse to a warrant to enter and search.
My view.
If the Police turn up (unannounced) without a warrant and 'ask' for permission to enter and search, it will be politely declined.
If the Police turn up (announced) without a warrant and "ask" for permission to enter and search, it will be politely accepted.
If the Police turn up (unannounced) with a warrant - they are not asking anything, and I will be in no position to argue the toss one way or the other ...