We do a lot of international work and I am very familiar with IEC standards.
First, the NEC and IEC are like comparing apples and oranges. NEC are not design standards, it is NFPA 70, and is to meet minimum safety requirements.
The IEC is more comparable in nature to IEEE which are equipment design standards. If you want a comparable document to NEC, i.e. NFPA 70, than you need to look at the British Standard BS 7671 called "Wiring Regulations".
So to your question: The fact the Owner wants you to follow IEC is doable. The equipment installed will still need to meet NEC and AHJ, which should not be an issue.
The bigger issue is that unless you expect to do short circuit studies based on IEC 60909 you are going to have an issue with ratings. There is to this day no cross reference for short circuit ratings between the calcs. They do their calcs using a different method that is not as conservative as the IEEE calcs. You cannot legitimately use IEC short circuit ratings on a system where the values were obtained by IEEE calcs. Typically, for any project in the US, manufacturer's will dual rate their equipment. If it is only labeled IEC, you will not be able to use it. (MCC components are notorious for this, watch out)
Frankly, whoever made that statement is a manager that has no understanding of electrical design, installation, standards, or equipment manufacturing.
As a side note, IEC standards are primarily based on manufacturers building their equipment anyway they want, and it be capable of passing the required tests. Conversely, IEEE standards are based on manufacturers building there equipment a certain way which means it will meet the requirements. Different philosophies. I will say, in general, IEC manufactured equipment comes across as not as heavy duty.
One last thing, IEEE does recognize IEC standards and has adopted certain ones instead of developing their own.