The data belongs to a US company, and is on servers which US based employees have access to. Those employees are beholden to US laws, and should retrieve the data if directed to do so by a US court.
Also the Irish company is a subsidiary of the US company. The Irish employees don't have to obey US law, but they do have to obey their bosses who in turn do have to obey US law.
So long as the data is stored on servers operated by an organisation which has a chain of command extending upwards in the US, they are beholden to the demands of the US government. The opposite probably wouldn't apply, as the Irish employees wouldn't have seniority over the US and thus couldn't compel them to do anything.
If they don't like it, the Irish part could be spun off as an entirely separate entity free of US control.