I don't think it's that worrying.
Ultimately, Murtough doesn't need Rangnick to point out the best candidates to him, they are obvious. Murtough will be well aware of the pros, cons, chances and risks.
I also think that Murtough will take Rangnick up on the consultations he will be getting paid for, even if it was first of all a financial agreement. He's by all accounts an admirer of Rangnick as a club runner, so he will be open to his input; but it might just be that the current agreement is for Rangnick to focus on the interim role as it is the most immediately important thing.
I also don't believe that Rangnick minds that he wasn't 'backed', I don't think he expected much investment into his 6 months stint, it's not something he would have done if the roles were reversed either.