No. Stainless-steel construction varies, and the complete base design matters. A shiny finish is not evidence of magnetic compatibility.
What the observation means
Some pans incorporate a suitable layer while others do not. A pan that works poorly on one zone may also be too small for that zone's detection requirements.
A useful next step
Check the cookware's stated compatibility and the hob's guidance. Use a known suitable undamaged pan for normal cooking observations. Do not assume an entire stainless set shares identical bases or attempt to solve incompatibility by overheating the pan.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.