Do some Schengen area countries share entry-exit data with the United States automatically?

As a follow-up to this question I asked a while back, a recent article on QZ claims

Despite holding valid visas and proof of being out of a restricted area for more than 14 days, some travelers are being denied boarding at Dubrovnik’s airport. They are receiving little explanation as to why, other than it is the US Customs and Border Protection (CBP) that is not granting them permission to travel to the US.

What is happening appears to be nothing more than a glitch, and travelers who have been denied visa clearance were eventually allowed on later flights (…)

As I mentioned in my previous question, this claim seems true, as it happened to a friend.

The article then quotes the CEO of APEX:

Joe Leader (…) believes European citizens leaving the Schengen areas and eventually heading to the US might not have their passport correctly scanned when leaving the Schengen area, even if they request a stamp, because that is not routine for European passports.

The lack of an electronic record delays the time CBP needs to verify the European citizens meet the requirements to travel.

How likely is it that this is the issue? I thought until EES comes into service, even Schengen area countries do not have an electronic way to check entry-exit records for other Schengen countries. Does the US CBP really have access to electronic Schengen exit records?

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Do EU countries share immigration information?

All Schengen countries share visa information through VIS. Denmark has also chosen to implement VIS. The central VIS system is linked to national systems, allowing Schengen states to exchange data. Sharing information regarding application decisions is particularly useful for preventing 'visa shopping'.

Do they check passport between Schengen countries?

Any person, irrespective of nationality, can travel between Schengen countries without going through border checks. However, national authorities can carry out police checks at borders between these countries and in border areas.

Are there border checks in Schengen?

There are no border checks between the Schengen countries.

Can I exit from another Schengen country?

Yes, you can enter or exit from the Schengen area via a country other than the one you have a visa for, your port of entry or exit doesn't depend on the issuing country of your visa.

[Question] How long is the data kept and who has access to it in the new European Entry/Exit System?

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