I am going to give the official ruling on this. If the scenario is from an ASL module, what is considered "provided by the game" is the counters in one copy of that module, plus one copy of every module required by that module (recursively). Counters from extra copies of modules/HASL you may own may not be used. If the scenario is from an HASL or similar, you use the counters from one copy of the HASL plus one copy of every requirement of that HASL. If the scenario is from another publication (e.g. ASL Journal, Schwerpunkt), unless the counters include ones that were not published in a module, you may use one copy of each module that is necessary to make up the depicted OB. If the counters depicted include counters from some other source, you may use one copy of that source in addition to any standard modules that are needed. Replacement counters must replace (not supplement) existing counters.
If you may have lost counters or are otherwise having trouble determining the number of counters that came in a particular configuration, you can view images of unpunched counter sheets on-line to get the information you need. Boardgamegeek has a good collection of these.
edit: unless you are a crazy radical like Klas.
JR