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We present a spectroscopic abundance analysis of the old, super-metal-rich open cluster NGC 6253, with emphasis on its O abundance. High-dispersion, 7774 Å O i triplet region spectra of 47 stars were obtained using Hydra II on the CTIO Blanco 4 m. Radial velocity analysis confirms 39 stars consistent with single star membership, primarily at the turnoff. Thirty-six of these are included in our abundance analysis. Our differential analysis relative to the Sun yields primarily scaled-solar values, with weighted cluster averages of [O/H] = +0.440±0.020, [Fe/H] = +0.445±0.014, [Al/H] = +0.487±0.020, [Si/H] = +0.504±0.018, and [Ni/H] = +0.702±0.018 (where the errors are σ_µ). We discuss possible origins for the three known super-metal-rich clusters based upon their abundance patterns, Galactic locations, and space motions. The abundance patterns of NGC 6253 are very similar to those of NGC 6791 and NGC 6583. With the possible exception of oxygen, the abundances of these clusters are all close to scaled-solar, and they are similar to patterns seen in metal-rich disk dwarfs and giants. However, they also seem to differ from those of metal-rich bulge stars. We demonstrate that NGC 6253 is unusually oxygen rich (in [O/H]) for its 3.3 Gyr age. While we find [O/Fe] to be scaled-solar for NGC 6253, the more recently reported values for NGC 6791 show a large variation, from values close to scaled-solar down to values at least a factor of two below scaled-solar. We discuss the possibility that the scaled-solar [O/Fe] abundances of NGC 6253 and NGC 6791 might reflect a flattening of the Galactic [O/Fe] versus [Fe/H] relationship. This possibility may be consistent with disk star abundance data, which show an apparent ''floor'' at [O/Fe] ~-0.1 for [Fe/H] > 0, and with chemical evolution model results, which may predict such a flattening due to a decrease in supernova Fe yields at super-solar-metallicities. Orbit solutions for NGC 6791 allow that it may have formed in the inner disk and was then kicked out, but the origins of the other two much younger clusters remain mysterious. We re-evaluate the age of NGC 6583 in view of the evidence that the cluster is super-metal-rich, and confirm a probable age less than 1 Gyr (best range: 500-900 Myr). We also argue that it is unlikely the cluster is more than 3 kpc away (best range: 2-3 kpc) if the apparent turnoff, main sequence, and giants are all cluster members.