The only explanation I see why it isn't work is because the app is in development mode, but apparently facebook removed that and replaced it with Access Levels.
You are indeed completely right!
The old system, consisting of Development Mode and Live Mode, has been replaced by respectively Standard Access and Advanced Access (cf. this documentation).
Apps in Development Mode can only request Permissions from app users who have a Role on the app or in a Business that has claimed the app. This is the same as Standard Access. Apps in Live Mode can request Permissions from anyone, but only if the Permissions have been approved through App Review. This is the same as Advanced Access. Features, although they cannot be requested from app users but are instead active/inactive, behave the same way.
This snippet was taken from this post.; Side note: They even wrote a paragraph about why they decided to switch and which features/improvements the new update brings - it's on the same site, just below the quote above
Anyhow, due to logistic reasons (supposedly) the update is only being pushed gently into the broad mass:
Access Levels are gradually being applied to all existing Business apps automatically.
You can find the banner on the previously mentioned site:
Summing up: Yes - the modes are actually replaced by their new "level system", though the update might haven't covered your Business app yet (but will so in the near future).