Because we output tons of other folks files, I can say with 100% certainty that color issues are 100% dependent on the file submitted provided the vendor has a solid profile.
Many times a "bad file" it's not even caught on the customer side-they may have an older monitor that renders weird, lack the proper PMS pallettes, set up files with CMYK and RGB mixed, have colors that look the same on screen but are defined differently, etc.
I don't know if we printed the above sign, but I can guarantee that if the printer has the ability to hit the pink in the type, it has the ability to hit the pink on the border provided it's given the proper information in the file. I'd bet that if you eyedroppered the copy and then the border, it's a different color all together, and possibly even one CMYK and one RGB.
Whether it's us, S365, 4over or whomever, unless you prep your files 100% using PMS swatches (that you reference to a swatchbook, NOT your monitor) or you have a perfectly calibrated monitor to your vendors systems, there will always be some color variations. It's inherent in the process.
As vendors, we can get close, and in our case we either do, or have schooled our clients to improve file setups for better color.
If anyone wants to ask a file prep question, I'm happy to help (even if we don't print for you).