Featherstone, after all, was the company's first artistic director, and made the radical "theatre without walls" initiative work, programming a body of work that drew from all aspects of Scottish theatre.
During Featherstone's tenure, the NTS developed more left-field artists alongside big main stage plays, an approach which Featherstone took with her when she became artistic director of the Royal Court Theatre in London. Despite heading up such august institutions, Featherstone has retained a Fringe sensibility developed during an era of politically driven grassroots shoestring companies and alternative cabaret.
Featherstone's first Edinburgh show in her own right was an adaptation of Gogol's short story, The Nose.
"The then literary manager at the Royal Court came to see it," Featherstone remembers, "and everything that's happened since came from that."
The latest recipient of Featherstone's open-minded approach to what theatre can be is Edinburgh regular Chris Goode, whose latest solo show, Men In The Cities, is currently running at the Traverse. The play is Goode's response to the murder of Drummer Lee Rigby, and to the suicide of a young gay man around the same time. Out of this, Goode explores the fear and loathing behind being a man in 21st-century society.
"Chris was on attachment with the Royal Court," Featherstone explains, "and he came up with this idea that sounded amazing, and which he wanted to bring to Edinburgh. Anything by Chris Goode appeals to me, so whatever he was going to do was probably going to be amazing. I think Chris is one of the most thrilling and honest performers ever, and when he did a reading of Men In The Cities, it was so raw and so honest about what it is to be male that it just made me feel really happy as a woman."
For Goode, although Men In The Cities is a fiction, it also comes from a pretty personal place.
"It's a pretty angry piece," he says. "I'm really interested in the ways in which we see men struggling to talk about certain things that are going on, and the ways in which men consciously hurt themselves and the people around them through a set of conversations that they're not having, and which aren't doing them any favours.
"There are conversations which I'm not having with my friends, let alone with the people I sit next to on the bus, but there are unpalatable things that need to be spoken. If there's one thing I've learned over the last 15 years, it's that theatre is a place where you can say those unpalatable things and know that the sky isn't going to fall in."
Goode's attitude fits in with Featherstone's ethos, both for what the Fringe should and could be and at the Royal Court.
"For me the Royal Court has changed immeasurably since Vicky arrived," Goode observes. "It's really good to be in a conversation with Vicky and everyone else there, and know that you can make something adventurous, even though you don't know what it's going to be, and that inspires you to push yourself to try things you might not have otherwise thought of."
Again, the umbilical links of this approach go way back, as was demonstrated by Featherstone's most recent visit to Scotland, for the funeral of David MacLennan, the producer, director, writer and performer who co-founded Wildcat Theatre in the 1970s after a stint working with John McGrath's 7:84 company. For the last decade, MacLennan pioneered the A Play, A Pie and A Pint lunchtime theatre phenomenon at Oran Mor in Glasgow.
"David was such a great, generous man," Featherstone says, "and just to be part of that community around him was a real privilege."
It is telling that Featherstone forged links, not just with pioneers like MacLennan, but with a newer generation of theatre-makers such as Goode, who continue to say important things with their work. In Featherstone's view, Men In The Cities is crucial in this respect.
"I think it's what the Fringe is for," she says. "It's about great artists like Chris taking a risk, challenging what entertainment means, and really surprising people in their honesty."
Men In The Cities is at the Traverse until August 24, various times.