Nah. Dandelions don't regrow stems; this can't be something done in response to being mowed. The plant doesn't think "I got mowed! I guess I'll grow a different way now".
Its a different growth pattern in the plant. Gotta be driven by genetics.
Dandelions are actually perennials so they will regrow stems several times, and survive multiple years. They will also tend to flower most abundantly in spring, but can re-flower in the fall.
Further, it's not just the stem involved, if your mowing regularly your taking out the leaves.
Yup the flat ones were none of those. They were really weird knarly mutated plants with exactly the same structure, leaves, stem and flowers as dandelion but grown flat and warped to hug the ground.
Its a different growth pattern in the plant. Gotta be driven by genetics.