You can still use that old PS you previously used to create those files.
You can, until that old PS becomes incompatible with your operating system and/or hardware. At that point only a subscription will give you access to your files, and you'll have access only as long as you pay.
You can still use that old PS you previously used to create those proprietary formats.
Again, that's true until that old PS becomes incompatible with your operating system and/or hardware.
As for the new PS CC subscriptions, what do you think is the difference between what you describe as "maintain access"/"access to the adjustment layers for later tweaking" and actually using PS ?
The point is that once CS6 becomes incompatible with your OS and/or hardware, continuous payment of a subscription is the only
way to access or use any of your proprietary Adobe files. Previously one could update or purchase only when necessary to maintain compatibility with computer operating systems and hardware. Under the new plan when your subscription runs out your files become useless until you renew.
 I'd think "access" means opening, viewing , printing, and anything that doesn't modify a file and "use" would mean things like "tweaking", adjusting, or anything that modifies a file. I'll admit it's a minor distinction and "access" might be provided by some 3rd party applications. Semantics aside, the problem is that you must
subscribe if your files are to remain useful in any meaningful way after CS6 becomes incompatible with your OS and/or hardware. That could take one year or five years, but it will definitely happen.