This is false.
A72: An attack does not always use the Attack action. Since Alchemist's Fire says you must use your action to use it, that's the action you make: the "Use an Object (Alchemist's Fire) action" if you will. As part of that action you make a single ranged weapon attack treating the vile as an improvised weapon, similar to how an Opportunity Attack uses a single attack but not the Attack action.
Now as for whether or not the vial that contains the alchemist's fire could be used as an improvised weapon as part of the Attack action using the improvised weapon rules, and what its properties would be: yes it can be used as an improvised weapon in the Attack action but what its properties are is up to the DM. A DM could fairly rule that the vial is solid enough that it only does bludgeoning damage similar to a light hammer when used in the Attack action. (Therefore implying using the regular alchemist's fire action would require taking time to throw it just right.) A DM could also fairly rule it works the same either way.