The Economic Policy Institute has a similar take on the numbers.
The issue is NEW LAYOFFS which is the subject of the report you posted. That is simple and evident and shown by every versioning of the BLS report and the various state UI departments. That is NEW LAYOFFS. The report says: "The labor force lost 539,000 nonfarm jobs in April,...
" It can't get more clear than that.
NOW, the 72,000 new hires are significant and good. But they do NOT represent a direct relationship to the "labor force lost" number.
If IBM lays off 7000 employees in April and Census hires 7000 people in April, while the two numbers WASH in TOTAL UNEMPLOYMENT, the two numbers are not directly related in that the same number of people would have been laid off, whether the Census had hired or not so the initial 7000 would have stood [the 539K number]
I think it boils down to the word LOST. Does it mean NEW LAYOFFS or does it mean added to the total unemployment figure [13.7M]. Backing up and trying to figure out the confusion I can see how it can be interpreted both ways, depending on how you view the data.
Historically the monthly report has been NEW JOB LOSSES. I can't see anything that suggests that has changed. On the other hand, if either WSJ or EPI made the comment, I can see the other taking lead from that and going with it.