Just the opposite. "Workers are getting sick in droves" would be analysis, and not appropriate. And if you read the article, the article wraps up with information that counters your claim that NPR is pushing an agenda about workers.

I think people are so accustomed to clickbait-y headlines, they see an agenda in the headlines of an organization that actually practices strong journalistic standards and plays it "safe" with its headlines, saying less than more.

Calling out sick implies using voice and not text to message their sickness, which is also analysis.

"Workers are using sick days, and businesses do not have enough workers not on sick days" is a plain jane version

Sure I have but neither the headline nor the article imply any such thing. I do not infer any such negative connotation from the title.

Is there another term for calling out sick that you believe doesn’t have such a connotation?

Aren't there usually a limited number of sick days?

My previous jobs have all given me a grand total of 2 sick days plus 2 personal days. Anything beyond that would have cut into vacation days.