I'm afraid this is an issue that is going to come up many times during your dd's childhood, PegsPigs. You'll decide you don't want her to have a particular item in her school lunch box, but other parents will put it in their children's lunch; you'll decide you don't want her to watch a particular DVD because she's too young for the age classification, but other parents will be less strict; you'll not allow certain behaviour, and other parents will - I went through this with all of my dses.
All you can say is, "I'm not X's mummy - if I was, X wouldn't have a Penguin in their lunchbox or be allowed to watch SawV either - but I am your mum, so you have to live by my rules. Yes, it's not fair. Yes I am the worst mummy in the whole wide world. You'll be allowed to do these things when you are old enough".
That said, it is always worth looking at your rules, with a critical eye, as you have done here, to see if they are ones you can relax without dire consequences. For example, for years and years, I didn't buy football shirts for the boys, because I hated them - the fabric, the cost, the way the clubs changed their strip every year, so you have to buy new ones, to keep up with everyone else.
Eventually, I gave my head a wobble, and decided I was being a bit daft - so I bought them a top each, via ebay, and then sometimes one or other of the boys got a new one as a birthday or christmas present. I still don't like them - but two of the boys (ds1 - 22, and ds3 - 18) grew out of wearing them, and buy really nice clothes now - only ds2 (20) still wears anything similar - and his are either the strips for his old hockey club or his University hockey club, or his cricket tops, from when he played cricket. They are still far too nylon-y and plastic for my liking, but he likes them.
I think that, relaxing this meant I could hang onto the rules that really mattered to me - particularly the age restricted video games. I was, apparently, the only mother in the known universe who didn't let her children play Call Of Duty - but I was OK with that.