How does a company deal with workers who belong to a union? That depends on so many things -- the history, the locality, the business, the workers and managment themselves. There can be a lot of reactionary dynamics from nearby unions and culture not directly in the employer and worker's union.
I can give no specific suggestion to the company -- short of a general suggestion to get smarter -- this nanny-policy is dumb and counter-productive for reason mentioned.
I think this article does not go far enough to explain what other measures the company has tried in order to get people to SHOW UP AT THEIR JOBS. If I was the business owner, I'd fire them for being in violation of company policies and deal with the union later. Perhaps this has been tried, we don't have enough information. I just know that absenteeism and misuse of FMLA laws is a huge problem for companies. Worker productivity can grind to a halt.