"Regarding admissions to hospital with gastroenteritis - it seems logical to say that the vast majority of cases of gastroenteritis in formula fed babies are going to be due to poor hygiene either in the preparation, storing and feeding of the formula"
Yes - you are right. And the high iron levels in formula also create conditions in the gut which make gastric illness more likely.
Babies are especially vulnerable to gastric illness, which is why breastmilk is such a good food for them - because of its antiviral and antibacterial qualities, none of which formula has.
But pointing out that the delivery method for formula the MAIN problem doesn't help much because parents who use formula are stuck with using bottles. When you're exhausted, you have a baby who's feeding little and often, you have other children to care for and a busy life, it's easy to see how mistakes get made with preparation.
On a personal note, I was so anxious about cleanliness and doing things right with my first (who I mixed fed while I was struggling with breastfeeding) I gave myself quite bad dermatitis from endless hand washing - worrying about keeping bottles and surfaces clean. Still got it 12 years later. 
So it's a bit 'pat' to just say 'as long as you keep the bottles clean and don't leave formula sitting around you won't have a problem.' The delivery system with formula is vulnerable to mistakes being made - it goes with the territory of bottlefeeding.
"I think if people have this attitude that BF prevents all illness"
I don't think anyone thinks this.