Definition:
Three vendors in a trench coat is basically a way of saying that a department or function inside a corporation is merely a front for a bunch of vendors trying to get as much money out of you as possible, rather than being a genuine internal department.
Explanation:
This is a corporate corruption of the classic three raccoons in the trench coat, which basically means a group of slightly deceitful critters pretending to be something greater and better than they are.
In a corporate world with so much outsourcing and so much cost cutting paired with the difficulty in getting and retaining internal resources, often support functions or other areas merely become a thin veneer of managers or permanent members of staff over a huge number of outsourced vendors.
This can mean that simple costs can escalate radically, and even asking for a minor item that should be classed as business as usual, can result in a hefty bill that you are not expecting.
Disclaimer: As always these posts are not aimed at anyone client or employer and are just my personal observations over a lifetime of dealing with both management and frontline associates.