Ten Hag's targets may turn out to be successes or flops, but they are at least sensibly recruited as opposed to the sugar-rush signings by managers (or Woodward) in desperate need of short-term success that may hinder long-term team-building. For that reason, I don't have a problem with Murtough approaching the role by pursuing players as instructed by Ten Hag, no more, no less.
It's in circumstances when a manager goes atfer those rash solve-all players as we've become accustomed that I would expect Murtough to take a bolder role and possibly overrule targets considered harmful panic-buys. Or similarly if there's no initiative on the side of the manager as with dithering Dave. Since neither of those situations has materialised, I'm pretty happy with how he's performed in the pretty calm circumstances -- obtained Ten Hag's targets without the drama, hasn't got in the way or caused rifts, and has shown discipline in spending this year (with the exception of Højlund, which in honesty doesn't bother me anyway).