Two physical therapy studies here suggest push-ups in slings are superior to ground-based push-ups and also improve function of the lumbar muscles. Low back pain patients respond well to muscle activation.

Here is a summary of the paper “Muscular Activities During Sling and Ground-based Push-up Exercise” published in BMC Research Notes 2014, 7:192

The study was aimed to compare muscle activities during push-up exercises performed undereither sling or ground conditions. The sling-based push-ups were found to induce higher muscle activities than the ground-based push-ups. The effects were more prominent in dynamic exercise, as compared to static exercise. The authors concluded that sling-based push-up exercise can provide greater activation in upper limb and anterior trunk muscles than the ground-based push-up exercise.

Here is a summary of the paper “Effects of "Push-ups Plus" Sling Exercise on Muscle Activation and Cross-sectional Area of the Multifidus Muscle in Patients with Low Back Pain” published in Journal of Physical Therapy Science 2013;25:1575–8

The purpose of this study was to examine the effect of lumbar stability exercises on chronic low back pain by using sling exercise and push-ups. Thirty adult subjects with chronic back pain participated, with 10 adults being assigned to each of 3 exercise groups: (1) general physical therapy, (2) lumbar stability using sling exercises, and (3) sling exercise plus push-ups. Each group trained for 30 minutes 3 times a week for 6 weeks.

The findings suggest that sling exercise plus push-ups are effective in activating and improving the function of the lumbar muscles.