I wouldn't doubt that someone on the inside tipped EA off to Take Two's plans for Codemasters... and EA felt threatened by whatever those plans are... in the end it just ups the price if Take Two comes back with another counter.
I can understand why EA is going for this deal. Codemasters has a lot of valuable racing franchises that could potentially help to differentiate their own portfolio in the genre. Need for Speed and Burnout is just a single spectrum of this, games like DIRT and F1 could work alongside them well. That said, I think both EA and Take-Two are bad choices from a client perspective as both companies has an awful history with milking franchises dry.