I’d argue branding and company culture are independent only if branding is weak in the first place.
Apple has a very strong brand, and if tomorrow they switched their logo and brand image to a cursive Ford style blue one it would need a strong justification behind it, a ton of employees would see such a change in a very negative way, and possibility think long and hard about their career path going from there, as the management might have lost their way.
Or the other way: when “Apple Computers” became “Apple” it wasn’t some random surface level change, but a reflection of how the company had deeply changed focus compared to its earlier days.
Branding and culture are rarely decoupled, and if any of those are strong enough they’ll change in lockstep.
PS: on brand and logo “refreshes”, like Peugeot moving to more a stylized lion, while those are arguably cosmetic, there is the same philosophy applied to the worker pool with “new blood” introduced to the company and processes and manufacturing moving along. In a way, the same thing is happening below and above the surface.