I came across a post that doesn't give the solution, but I just saw that you already went there this morning ;-) I think the person who said it's possible, didn't know about Document Manager...
Looking for BOM on this page (which lists all the Document Manager commands a priori), there are only instructions like "access" or "get", but nothing to create, sorry:
http://help.solidworks.com/2015/english/api/swdocmgrapi/SolidWorks.Interop.swdocumentmgr~SolidWorks.Interop.swdocumentmgr_namespace.html?id=30a118bab16d4ebdb948d29c74dcfd9f#Pg0
Or by searching for TABLE and looking at the members on this page (expanding with the +), we find nothing either:
http://help.solidworks.com/2015/english/api/swdocmgrapi/SolidWorks.Interop.swdocumentmgr~SolidWorks.Interop.swdocumentmgr.ISwDMTable_members.html?id=b4f08e90682443dd91ef867afd8a2192#Pg0
A priori the link below is only useful when the file is opened, isn't it? I think that's what you're going to have to do.
http://help.solidworks.com/2015/English/api/sldworksapi/Insert_and_Show_BOM_Table_in_Assembly_Example_VBNET.htm
Or another capillotracted solution, is to go through all the SolidWorks tree to create your table and recreate it as a text file...
By the way, are you sure SmartBOM doesn't open the file?
Edit:
A response from someone who uses the Domcument Manager to confirm my words:
https://forum.solidworks.com/message/467937#467937
It goes through all the rooms well...
Edit 2: it can be dangerous to create the bill of materials without opening the file, because if one of the components has been modified (change of code, material, in a welded machine, etc.) without updating the assemblies that contain it, your bill of materials will be wrong!
Edit 3: a solution could be to include a bill of materials in the models of your assemblies, at least all the new assemblies created will not be a problem!