If someone works for a firm owned by a Jew who presumably does not sell the chametz, as he is totally secular, may one drink Diet Coke from that fridge?
Sidestepping the issue as to whether or not diet soda uses artificial sweeteners or corn syrup, lets go with the assumption that it's corn syrup.
Yes you can drink it, because corn (and its derivatives) isn't actual chametz, so there is no obligation to sell it during Passover. Therefore a can of soda is permissible even if it wasn't sold during Passover.
Source: Halachipedia on Kitniyot
As to whether or not there might be some secret ingredient that is potentially chametz. This isn't an issue as the halakha is very clear. Once something becomes non-edible, it loses its status as food and can therefore be added to food and consumed, even if it came from a totally non kosher source. Therefore pig gelatin can be consumed, even with dairy. These "secret ingredients" or flavorings, are also not food. While there are stricter opinions that disagree with these halakhot, it does not take away from the fact that one will have very large poskim to rely upon, such as the Shulchan Arukh (YD 99). Most Kashrut agencies have policies in place to not follow these halakhot, but the actual halakha remains the same, despite their own internal policies.