We don't but I only linked it out of interest. If a 262 was in the transonic range (and still in one piece!) then speculatively a rocket boost could have pushed it over the line even if the turbines had flamed out.

There is another claim that Heini Dittmar went supersonic in the Me163a V4 that I think was also flown by Hanna Reitsch.
He is now well known to have officially reached 1004.5km/hr in the rocket plane and had throttled back approaching this speed due to buffeting.
Mano Ziegler who was a friend of Dittmar apparently wrote in his book Me163 that the rocket went supersonic and that sonic booms were reported on the ground.
The 163 had a 14 percent thick wing root and 8 percent at the tips.
Dittmar lost control on his 1004.5km/hr flight.
On 6 July 1944 Heini Dittmar reached with the comet Me 163BV18 VA + SP a speed of 1130km / h

There's an intriguing piece of film footage from the Lippisch archives of a P13a gliding in for a landing in a hilly region of German occupied territory in 1944 or 45.

http://www.youtube.com/watch?v=MvtxjSrImHw

Although the DM1 apparently never flew, at the very least a large glider mockup of the P13a did fly as this video obviously demonstrates.
Notably, the P13a in the old film sports the ramjet intake nozzle and seems to sport the walter rocket exhaust nozzle at the base of the tail. It has the forward landing bulge skid under the nose and many of the production features not integrated in the DM1.

Nice footage. Must have been exhilarating. You have to love building airplanes. I wonder if it was a glider or a working prototype, maybe on a jet engine for airframe tests, or maybe a full prototype.

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"What might work in New York City is certainly not going to work in Montana. So, for the federal government to be having any kind of, you know, blanket rules that they're going to try to impose, I think doesn't make sense." Hillary Clinton

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What the youtube above means is that the designers were ok, only they were working for the wrong boss...

That wind tunnel with all that trestle wood like I have in my shed is priceless!

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Everly Brothers - What I Have To Do Is Dream
"Never wrestle with pigs, you both end up getting dirty and the pig likes it."

You have a wind tunnel in your shed... I am on my way.

__________________
"What might work in New York City is certainly not going to work in Montana. So, for the federal government to be having any kind of, you know, blanket rules that they're going to try to impose, I think doesn't make sense." Hillary Clinton

(Photo removed for humanitarian reasons.)