which game has the closest real life story

[Alakallanar]

For a start, point&click adventures set in the present (or the recent past) without fantastical elements are probably good candidates. For example the already mentioned L.A.Noire.

Or something like Europa Universalis or Crusader Kings perhaps? Although these ones don't really have a story.

[Damajin]

Postal, easily.

[Yvaelle]

Portal - it just hasn't happened yet

I suppose. I guess something like Transformers Devastation doesn't even put up the facade of being real. CoD: MW kind of does, which makes it's deviations stand out as utterly fantastical.

To me, it just kind of stuck out because I remember playing CoD4 and thinking "wow i'm glad this was made", then played MW2 and thought "did Tom Clancy write this", and then moving onto MW3 and thought "did a team of Tom Clancy's from across the multiverse write this?".

You were wise to avoid Ghosts and Advanced Warfare, then