Inno Setup does not seem to write to the registry on a 64-bit machine
Finally solved it.
Inno Setup was running as 32bit on a 64bit machine, hence HKLM correspond to HKLM\Wow6432Node.
I need to add check for IsWin64 and use HKLM64 in that case. I think the syntax should be:
Root: HKLM64; ... <Subkey, Flags, etc.> ... Check: IsWin64