Way to tell how many times a game has been given away? [GA inside]

It should be quite accurate as it will show any GA made for that game regardless of region restriction, group requirement or level. Many of the GAs are likely either bundled games or low cost non-bundled games. Higher dollar non-bundles that have not had significant discounts are less frequent simply because they are not as easy to come by for the average consumer to simply give away large amounts of. However even these get a decent showing sometimes (as in Resident Evil 7) just no where near as many as the more affordable bundled / high discount games.