Whilst reimbursement will happen for emergency care delivered in the EU, it's a risk, if you consider how much that could be.
In Italy, my neighbour's partner stepped backwards to allow someone to pass him on a pavement, to fall down a 6ft hole, breaking his back. He was incredibly lucky not to be paralysed, but he did need lots of x-rays, scans and so on, not to mention several days inpatient treatment, before being medivacced back to the UK, on a chartered aeroplane, with him the only passenger, and the care team of a doctor, nurse and technician accompanying him. My neighbour had to book herself a scheduled flight home, as neither were able to return on the flights they had booked.
I'm sure that bill would have been a lot to settle, before being discharged, without the hassle of all the necessary arrangements and the time out of pocket.
Clearly, we all decide how much risk we will underwrite for ourselves.