I double-checked everything. All my steps turned out to be incorrect. And the problem is actually less complex, but hard to check it: if I save game on the Gargoyles Lair level, then simply exit the game, re-enter, and try to resume from the save, the problem returns.
So, if you play through all the levels from Mediva group in one go, everything works. But if you save in a secret level, finish the game, and then restart from the saved game in the secret level, you won't be able to complete it.

The only way to get around this problem is to have a save at Mediva1 map before entering the secret.
Then it's possible to go to secret level, completed it, return to Mediva1 and complete it, and go to Mediva2 map. Whats all.