The ASRDATA line does not affect the display state of the map, but allows to limit the display of items within the map based on the ASR file. An example use case would be two versions of an airport layout, where a single map would for example contain taxiway identifiers for both versions, but draw only the ones relevant to the currently open ASR file.
To display map data in only a specific ASR file, you need to use an ACTIVE line to activate the map automatically and the ASRDATA line to limit the drawing to the wanted ASR file. The map itself will be active in all ASR files, but will only draw anything on the one specified ASR file. Whether that is useful or not, depends on the situation.