I don't believe EK promise a time to command, they just tell you what the current state of play is.
However, looking at the numbers and assuming no increase in the expansion rate, you are probably not far off the mark. We are planning to have 2100 pilots, lets assume that 1150 are captains to allow for management, training etc. Right now we have near as damn it 1000 pilots and are expecting to hire a couple of hundred DECs over the next year or so.
The average age of the work force is pretty low, so best case would be 50 retirements by 2012. So we probably have now about our quota of Captains within the company to be supplemented by DECs. This would mean that 7 years might be optimistic, as we have all the Captain candidates we require until 2012, unless the expansion accelerates. Conversely, if the upgrade rate slows and the DEC recruitment rate increases even guys in the company now might be hurting despite the hollow sounding assurances from management that no one will be disadvantaged.
Hope that helps, not exactly optimistic but best guess right now, who knows what might happen in the future.
Cerberus