Ok it sounds like she phrased this badly.
She is advising you to have your baby in hospital.
She cannot insist you have your baby in hospital.
You can still choose a homebirth with a pool if you wanted, or if you wanted the birth centre, ask them. The VBAC greentop guidelines are worth a google, and generally women who have had a section are supposed to be treated the same as any other woman.
But, the birth centre can refuse you. It may be a good idea to have a think about what you want, and have an appointment with a Supervisor of Midwives to discuss how they will support you.
I would also suggest you consider the risks of having a monitored VBAC in hospital. You can accept of decline any constant monitoring they offer of course.
Who gets the last say? You do.
You can decline anything you are not happy to consent to. But they can decline things too - like access to a birth pool, birth centre etc.
The cannot go beyond the due date is really a load of rubbish - generally it is very unwise and risky to induce after a previous CS - the risk of uterine rupture increases hugely. So it would usually be waited for spontaneous labour, and perhaps book a date for repeat CS at 42 week if baby has not arrived.
Have a look at the Yahoo VBAC HBAC list - lots of fab wise women on there who can help you right accurate information.