Delay of game. Clock starts when?

[Mike Simonds]

Rule 3-4-3i. The clock starts on the snap when the penalty for a delay of game foul is accepted.

Last Saturday, the referee started the clock on the ready after a delay of game penalty was assessed. The reason given was that the clock was running (previous play was a running play that ended inbounds).

My question is this: Does the referee have the authority under the rules to start the clock on the ready after a delay of game penalty is accepted? If so, what is the rule reference? I always thought that the clock starts on the snap after every delay of game foul if it is accepted.

Carpe Diem!