When credentials are mapped to a scanning target, the global credential is indeed the last one to be tried. In theory it doesn't matter how many incorrect credentials are tried on an asset. As long as one works there will be no errors.
You could try and restart your Lansweeper server service. This will clear the cache and force Lansweeper to first check the mapped credentials when scanning an asset, and only if none of those work, try the global credential.
Should you have an error regarding a credential on your asset's page, and you are sure you have the correct credential mapped (a credential with local administrative permissions). Then I would start looking at your firewall or other settings which might be blocking WMI access.
You can also do a test with testconnection.exe, which can be found in Program Files (x86)\Lansweeper\Actions on your Lansweeper server. Perform the test from your Lansweeper server to the client machine, submit the same credential used by Lansweeper to scan the client.