It isn't as black and white as would you buy a bottle or not there are so many other aspects you need to consider.
When ds first wanted to drink it was with his immediate group of friends - he is, and they are all, pretty sensible and they wanted to have a couple of drinks to socialise in someone's garden, and he has continued to not hang about in groups in popular areas (here it is edges of fields/golf courses hidden near trees usually) which end up as 100+ teenagers mingling, where kids get pissed and leave a mess for the landowners to deal with week after week.
There is a range of ages there right up to 18 year olds that he just does not feel comfortable in as there is constant drama, some are smoking, there is cannabis and other drugs, occasional fighting, lighting "camp" fires etc there has been accidents and kids ending up burnt in A+E, there was even once one of them showing off a knife. It all starts well before 8pm and initially seems harmless but escalates over time. I would worry the beach is your local spot for this kind of trouble and 14 is just too young for it.
If there is no one else there why does she want to go and why does she want to show off she has alcohol? You are not getting the full story.
I would hold off her attending these things (with or without alcohol) until at least next summer if possible, and encourage them to meet up in less popular, safer places or gardens instead with their friends of their own age only.