That is just excuse from a print house that the files are somekind wrong ( or coated uncoated paper theory is just nonsense ). You should explain to your client that the printhouse or pre-press manager are just messing with him . Main reason for changing the color is the paper color . Open any paper manufacturer , you’ll notice that every paper got description of being more white , grey , blue or even yellow . On bottom lane , incompetent management at the printhouse leads to coated uncoated versions 
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Maybe, but…
The difference in appearance between how something looks printed on uncoated vs. coated paper can be quite significant. It can look darker, more washed out, a bit cooler or warmer, or lose its vibrancy, but yeah, you’re right, the color itself generally doesn’t shift much in most instances if the paper color is the same.
However, I wouldn’t jump to conclusions about placing blame on a less-than-honest printer. Remember, we’re reading what Mojo wrote about what the client said that the printer told him about something we haven’t even seen ourselves. In other words, there’s lots of room for incomplete information in all of this. 
I provide all those files to my clients, who are nonprofits and small business. Most have no one in house to deal with them. I provide a small brand guide. Never had issues.
I figure:
- if you don’t supply all the files they need (organized and carefully labeled for them and with an explanation), they won’t necessarily know or remember to come back and ask you about what they need when printing on different types of stock, so they could use a wrong file that they do have; and
- most clients are probably printing on UNcoated stock most of the time, so the designer cannot assume that coated stock is the default. If anything, it might be safer to assume the default is UNcoated.
It can be a major issue if the chosen colors are ones that shift quite a bit between uncoated and coated, such as yellow > orange and blue > purple.