At the end of the day its a 'show' and the stars are the dragons, they clearly edited it to show you coming across as a bit prickly which gets people talking and reacting which it did and you have benefited.
A friend of my uncle was on the show a few years back,some of you might remember he got into a bit of an argument with Theo over sun bed towels for luxury liners etc, he alienated then completely and it became one of the highlights of the series.
His orders for them went through the roof and they did very well out of it and you can actually see them on sale now in places like Debenhams and airport shops, he actually used the show and his 'performance' as marketing tool in his advertising etc. He has something on the packaging like 'as seen on Dragons Den'.
By the way he's a very nice and not at all how he came over in the 'show', so my uncle tells me anyway.
They probably miss out on most of the best opportunities pitched to them as they can not be expected to understand all markets no matter what they might like us to think.
Incidentally my brother knows Deborah Meaden (and family) quite well, he does/did business with them in the entertainment field her family owned holiday parks he used to supply the slot machines etc to them, things have moved on a bit since then of course but he says she is a very nice lady indeed.
I have no doubt you will do very well out of this and at a quick glance I like the business model, if it was franchised in the UK it might even look at it myself for my daughter.
Are you aware of the 'Handbag Clinic' in Chelsea who do something similar ?