I'm looking for a specific idiom/metaphor used in a business context
Solution 1:
self-praise is no praise TFD an idiom
praise of oneself is inherently worthless or dubious, as one cannot be objective of one's own work or accomplishments.
As in:
So many companies claim to be the best in the business at this or that in their marketing, but self-praise is no praise, so I can never take them seriously.
Like self-assertion, the act of putting forth your own opinions in a boastful or inconsiderate manner that implies you feel superior to others works for some, but in business it sows doubt.