Ask them one simple question - "how has digital affected the concept of leadership?".
In the 19th century you scaled a company by adding people. Companies grew into massive organisations of tens of thousands and leaders couldn't hope to know each person individually, so they applied broad concepts.
The 20th century brought in machinery to replace human muscle. Many of the remainder were book-keepers and clerks, but in the latter part of the century these disappeared too and companies shrank to a core of knowledge workers.
But we were still living in a physical world. Making changes in physical infrastructure is expensive and systems were created to deliberately slow the decision process down and make sure it had buy-in at the highest levels. This slowed progress to a crawl and the static company became normal, with change as an exceptional event. Managing this slow change process became the core skill for executives.
These are the skills most coaches teach. How to survive in 1960s companies where facts were hard to obtain and thus opinions held sway. How to prepare reports which bludgeon change ideas through and manage all the attempts to derail this change. And how to "lead" remotely through edict.
Compare this with the digital world. Here, like a 24 hour newsfeed, things can change continually. There is a constant feed of data to work from. Small teams of experts, often geographically remote, are the way to make things happen and the timescale to do so is measured in minutes, not months. Change is default and static - even for a moment - means falling behind.
Leadership in this digital world is about enabling and co-ordinating teams to release their potential, not bullying them into doing what you have decreed is right. It is about championing them to other stakeholders to ensure they have the resources and backing they need. Keeping everyone up to speed with continuous changing of procedures, capabilities and possibilities. Sifting a deluge of knowledge to ensure what is truly relevant reaches right person at right time.
In this world, "need to know" information, management by memo and setting fixed policies - all key planks of old fashioned leadership - will hold you back.
If your coach has experience in a large 20th century company, his/her problem will be unlearning this. They may have some nuggets to impart, but the general flow will be in the wrong direction. They can seriously damage your company.