To say choosing a profile is "no big deal" to say that all of the tools used to get accurate colour in today's printing are unimportant and billions of dollars were wasted. A profile is made for a particular mix of paper and ink. It controls the actual amount of each ink. So a different profile gives a different amount of ink, and a different colour.
Your printer might be saying "my customers can't tell one colour from another so it doesn't matter".
Your printer might be saying "I can't tell one colour from another so it can't matter".
Your printer might even be adjusting the ink levels on the press to make things look nice. This is a valid way of working, and 20 years ago was the main way of fixing colour. But he should say so. It also means you cannot get beyond the level of accuracy you have today as any attempt to fix it will just be adjusted on the press.