I found a website that you might find helpful. It's at www.schengenvisainfo.com
. One part in particular seems to address your question. Here it is:
"US Citizen Rejected from Entering Europe Visa-Free
As previously stated, if you were rejected from entering the Schengen Zone, despite of being a US national
or a national of a country that has established visa-free regime with the European Union, you will need to apply for a Schengen visa in the United States
You can apply for a visa at the embassy or consulate of the main country you wish to visit, located in the US
. Sometimes embassies outsource visa submission to the embassy or consulate of another Schengen country or third parties that offer visa services.
For more information, read the article “How and Where to Apply for a Schengen Visa in the US?"
Thus, even though US Citizens are exempt from the Schengen requirement, that first paragraph clearly contemplates that US citizens are sometimes denied entry without one. Elsewhere in that website it says the decision of the official is final, and your only recourse is to return to the US and obtain a schengen visa from the the embassy or consulate of the main country you wish to visit, located in the US
That would explain why potential employers want you to obtain a schengen visa before they employ you.
I suggest you read through that website carefully and completely. It is very informative.