Effects of weight loss interventions for adults who are obese on mortality, cardiovascular disease, and cancer: systematic review and meta-analysis

Could the mortality reducing effect of weight loss interventions be partly, or in total, explained by increased exercise?

In the Supplemental Appendix Table 6 (p. 34 point 1.8) it is shown that weight loss interventions not including an exercise program did not convincingly reduce mortality 0.78 [0.44, 1.37], I² = 0%, p=0.38. Whereas, weight loss interventions including an exercise program did significantly reduce mortality 0.84 [0.72, 0.97], I² = 0%, p=0.02.

The authors conclude that "Weight reducing diets, usually low in fat and saturated fat, with or without exercise advice or programmes, may reduce premature all cause mortality in adults with obesity".
However, the data only support that weight loss interventions, not solely weight reducing diets, reduce mortality, and the subgroup analysis does not robustly support that interventions without exercise programs reduced mortality even though this is concluded in the article.

The authors could have discussed the apparent importance of including proper exercise programs, and not only advice to exercise, in weight loss interventions.