The documentation is describing how "Push" translations are resolved. That is, where you have chosen source content in a high publication to be translated in one or more lower publications lower in the BluePrint. In this case, Translation Manager will use any components which have been localised in any intermediate publications as a source. This is because, for example, there may be some regional localisations (mph vs. kph or left hand drive vs. right hand drive in an automotive use case) that need to be included in the requested translations. Without including them, any existing localisation would be skipped and the returned content would be translated directly from the top level.
The reason that Translation Manager skips localised items with only one version is because a localised item immediately becomes version 1 before modification, i.e. it has been localised but no changes have been made. If a localised item has been modified (has a version number of 2 or higher) it is used as a source, this is what is meant by:
"Localized items are always valid inclusions, except when the item has
not been translated (an item is considered to have been translated
when it has version 2.0 or higher)"
Perhaps the documentation could be worded a little clearer - something like:
"Localized items are always valid inclusions, except when the item has not been translated (an item is considered to have not been translated when it only has a version 1.0)"
TM does not check for changes made by the MTSUser - That may not be the user that TM is running as and/or TMS may not be the only process changing data as that user. TM does maintain some data (I think it's stored as AppData) to keep track of what items were translated as part of which TM jobs.