  For the past three decades, and until recently, there has been a serious
discrepancy between the observed and theoretical values of the apsidal motion
rate dw/dt of the eccentric eclipsing binary DI Her, which has even been
interpreted occasionally as a possible failure of General Relativity (GR).
Recent observations of the Rossiter-McLaughlin effect have shown convincingly
that the reason for the anomaly is that the rotational axes of the stars and
the orbital axis are misaligned, which changes the predicted rate of precession
significantly. Although as a result of those measurements the disagreement is
now drastically smaller, it remains formally at the level of 50%, possibly due
to errors in the measured apsidal motion rate, outdated stellar models, or
inaccuracies in the stellar parameters. Here we address each of these issues in
order to improve the agreement further. New times of minimum have been
collected in order to redetermine the apsidal motion rate. We have computed new
stellar evolution models with updated physical inputs, and derived improved
apsidal motion constants for the components. We have performed Monte Carlo
simulations to infer the theoretical distribution of dw/dt, including the
contributions from GR as well as tidal and rotational distortions. All
observational errors have been accounted for. Our simulations yield a
retrograde apsidal motion rate due to the rotationally-induced oblateness of
-0.00056 deg/cycle (mode of the distribution), a GR contribution of +0.00068
deg/cycle, and a tidal contribution of +0.00034 deg/cycle, leading to a total
predicted rate of +0.00046 deg/cycle. This is in excellent agreement with the
newly measured value of +0.00042 deg/cycle. The formal difference is now
reduced to 10%, a small fraction of the observational uncertainties. (abridged)
