Indeed they do!
Based off testing with a GPS acceleration monitoring device and comparing with a number of different results from all the other DC stock (desiro [444 and 450], desiro cities [700 and 707], electrostars [377, 378, 387, 376], networkers [465 [both motors], 466], junipers [458], 455, 777, the 701 is the fastest accelerating 100mph DC unit in the country, and the second fastest accelerating DC unit behind the 777, which is comparatively geared for 62mph (higher top speed gearing = slower acceleration and vice versa) (although I don't have data for the 710, so it might tie with that or be third because it has 90mph gearing).
It beats even the similar Desiro Cities (on DC of course) by a decent margin, especially when it comes to sustained acceleration at higher speeds.
It seems that the data provided on wikipedia is often wrong. The case with the desiros anyway is that the 0.85 figure is actually the AC acceleration rather than the DC, but this isn't specified on the Siemens specification sheet for the unit/s. Obviously they're trying to sell their product so they'd attempt to get higher figures in there without technically stating the power mode.
For the Desiro units, e.g the 450 and 444, they wouldn't ever be able to get to their advertised 1m/s^2 rate as they have such high power draw, meaning that the sub stations are unable to cope and therefore the power has been reduced significantly over the years. They’re quite close, but still behind.
In short, SWR’s “better acceleration” claim is indeed true after all, and to quite an extent as well.