A clinician told me Nuera Skintyte would not work for me because the skin I want to tighten has no fat under it. Is that true?

I'm wanting to get rid of cellulite and some sagging on my bum, thighs, batwings, and belly after losing 30lbs (166 to 136lbs, 5'4" 37 years old 23% BF now). There's a TAD bit of loose skin on my inner thighs from pregnancy related stretch marks as well as wrinkling on my lower belly, no cellulite on arms. The lady who looked at me said I am not a good candidate because there's no fat under these areas (but my thigh and bum jiggles alot and my major cellulite beg to differ). Is this accurate?