I'm pretty sure you have a flaw in your data. This is what I get when I search for "Restore our Future" on this page:
To me, that looks like you're failing to account for the "Oppose" value in the "Support/Oppose" column. They spent millions on opposing Obama, but that still counts as spending money on him for filing purposes. You can't just flip the result, though, because slightly further down they have spending against the Republican Newt Gingrich. Better to break the data down into the four combinations:
- Support / Republican -> Solid red
- Support / Democrat -> Solid blue
- Oppose / Republican -> Striped red
- Oppose / Democrat -> Striped blue
As to the title question of whether a Super PAC can give to both sides, there is nothing to prevent them from doing so. The only restriction on how Super PACs spend their money is that they may only make Independent Expenditures:
An independent expenditure, in elections in the United States, is a political campaign communication that expressly advocates the election or defeat of a clearly identified candidate that is not made in cooperation, consultation or concert with or at the request or suggestion of a candidate, candidate’s authorized committee or a political party.
Additionally, these Independent Expenditures can't be contributions directly to a candidate. (Further reading) (I assume in your question when you say contribution you actually mean expenditure on behalf of, since direct contributions aren't allowed.)
There would be little point in both supporting and opposing the same candidate, but nothing stops a single-issue SuperPAC from supporting anyone who espouses their views and opposing their opponents, regardless of affiliation.