Your data shows that the Republican Majority Campaign has given millions to Democratic candidates. OpenSecrets.org's website shows 100% of their contributions going to Republicans.
Who is correct?
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I agree that it's confusing--there are a lot of non-obvious intricacies to campaign finance data. In the case of Republican Majority Campaign and Obama, the spending was on independent expenditures against Obama. If you download the data from here:
you'll see a column called transaction_type. The FEC tracks a variety of different types of transfers and expenditures beyond simple donations. The transaction_type field encodes that information. In this case, the transaction type is '24A', meaning independent expenditure against a candidate. '24E' would be an independent expenditure supporting a candidate. A full list of transaction types is available from the FEC:
You might also want to read this blog post on using TransparencyData:
It doesn't cover the specific issue of independent expenditures, but it will give you an overview of the various complexities to keep in mind when working with this data.
I hope that clears things up somewhat.