I’ve read elsewhere (Steve Trimble’s Dew Line) that Boeing cannot offer a 767-300 or 767-400 fuselage because the longer length means a shallower takeoff rotation to avoid tail strike, and that translates to longer than the specified 7000’ takeoff requirement of the SRD
Now there is a little tid bit that I haven’t seen before. Kind of points out that the two engine solution does have its negative side, unless you blow out the takeoff distance requirement, and if you can tail strike for certain it will be struck by someone somehow.
Re: 767-400 (or even 767-300): We specifically asked the question about the 767-300 of Boeing at its tanker briefing at the Farnborough Air Show. The response was that the longer fuselage means the airplane would require a shallower rotation to avoid a tail strike (or in this case, a tail-boom strike). This means a longer take-off run and a longer runway requirement. The USAF specified a 7,000 ft runway requirement in the first RFP (and this is unchanged in the second).
Use of the 767-400 would only aggravate the rotation/take-off roll situation.