I also think he's got a valid point. Perhaps any pilots loitering here (Pin Head incl.) could give us an idea of what a SID change might involve? I've had pilots complain about a change of runway / SID which has required them to reprogram FMC or rebrief for at least a couple of minutes, and that's before taxi. I'd be extremely loath to force them into that on an active runway.
And a change from a heading to a SID doesn't sound like a last minute safety issue, more like the lifting of a previous restriction back to standard ops (assuming that the airport usually uses SIDs).