Not wrong, entirely.
According to the U.S. Department of Labor, Bureau of Labor Statistics, negative responses to all of the following questions (A) & (B) below, count the person neither as employed or unemployed.
(1)Did any work for pay or profit during the survey period, whether full-time, part-time or temporary or
(2)would have met either of those conditions except for, vacation, illness, child-care problems, other family or personal obligations, maternity, labor dispute or inclement weather.
Does not meet any of the employed conditions and:
(1)Had a job interview,
(2)Contacted an employer, employment agency, friend, relative, of school employment center about a job,
(3)Sent out a resume or job application,
(4)Answered a job advertisement,
(5)Checked a union or professional register, or
(6)some other active job placement acivity.
So if someone answers no to (1) - had not job interview, found no notice of a prospective job (4), after months of weekly checking with (2) did not recheck with them sduring the survey week, and thus found nothing new for (3), and is neither a professional or union member (5) and has tired of emploring friends, relatives and neghbors for help or suggestions (6) and has thus given up, they are not counted as "unemployed".
Now, maybe my use of the term "registered somewhere as actively seeking employment was too limited" (my Alzheimers from knowing the regs), but the spirit is the same - those who, for any number of reasons, are considered by the methods of the Department of Labor as not employed and yet not "actively seeking work" are not counted as unemployed. An unemployed person who has given up is not counted as unemployed.