One of the twins was looking at a mug. He touched it but it remained on the hook. The other twin was happy playing with a car from the store..
And yet
A staff member behind me told me the children were very naughty and we should not be allowed out in public if I can't control them. She said they're behaviour is awful
That's just not consistent. No one watches a 3yr old touch a cup on a hook, then leave it, whilst another 3yr old plays with a toy car, and views this as children who shouldn't be allowed out in public.
You're not giving the full story OP. Or maybe more that you're not seeing it.
They were being loud but were excited.
This little sentence is going to be a lot more relevant than you let on. Maybe there's an element of, don't play with a stock toy if you're not buying it, but again, that doesn't prompt a "you shouldn't be allowed in public" level of response.
And seeing as you are insistent that you didn't exaggerate what she said, then for her to make a comment like that. People don't tend to comment. Maybe glares, or tuts or shakes of heads, but the Great British public are renowned for not confronting, so for her to say something so strongly like this, they were really not behaving in an acceptable way. And it's not because one placed their finger on a mug.
Did she watch one child go to take the breakable mug (so it would have been more than just a quick touch) as you weren't watching him, and initially alert you with a loud "Careful there young man?"...and then perhaps receive a "don't tell my child off" glare from you, which would have then understandably got her back up? Whilst they're both simultaneously "being loud" (yelling/shrieking/screaming/shouting).
You are really defensive OP. You asked a question and you don't like the answers which suggests you are not willing to accept that most people viewed your scenario as your children were badly behaved and you didn't parent that. The vast majority are telling you (that whilst they wouldn't have been as rude and direct as the shop assistant) that they can't stand this kind of behaviour from children when the parent is not addressing it.