Sounds good as long as the firm that's doing it does employ qualified slaters that understand 'random' work (a proper rarity these days and getting rarer!).
The problem with the use of underfelt, when nailing direct to sarking, is pretty counter productive really as each and every nail pierces the membrane. On a well laid roof that can have its problems with widespread, unobtrusive little leaks causing damage over time.
What I would recommend is counter-battening on top of the sarking board, then underfelt and then slate lath (battens) on top of that - especially with shoulder nailed Burlingtons (ballachulish are 'head' nailed).
Believe me, the extra cost would be negligible when weighing up the long term alternatives.
And again, not wanting to sound too pessimistic; many officials in safe positions behind high desks do not always know what they are talking about, particularly when it comes to the end product of skilled trades - they rely on 'The Book', Insurance safety nets, ISO's, BBA's and the like . . even Historic Scotland can get it wrong when it comes to slate roofing!
A sign of the times I'm afraid - but look on the bright side, there are a few good uns still about and I'm sure you'll find them.