1) Since the labor force participation rate includes both employed and unemployed but looking for work, by looking at that statistic alone, you know nothing about what % of men or women are unemployed.
2) In fact, as of 2008, the most recent data I found on the BLS site:
http://www.dol.gov/wb/factsheets/Qf-ESWM08.htmthe numbers of men and women employed are NOT "roughly equal."
The numbers are:
67,876,000 women were employed as compared with 77,486,000 men; 3,196,000 women were unemployed compared with 5,033,000 unemployed men.
And, as the whitehouse.gov report you liked indicated, the primary reason why men's unemployment has increased more than women's during the recession is that they are much more likely to be employed in occupations and industries that are sensitive to business cycles, e.g., construction. People who don't want this factor accounted for then should be equally comfortable with ignoring factors that partially account for the pay gap, e.g., industry.
This info also implies that, as the recovery continues, men will see a greater employment increase than will women.
These statistics also don't account for the number of underemployed, e.g., people who are working but only part time, but would prefer to work full time. Since a larger proportion of part time workers are women, looking only at numbers employed vs. not employed isn't a complete picture.
Etc., etc.