Phillip Rivers spikitis may have caused loss

My son Dan says I need to write about a clock mistake made today by Phillip Rivers, the SD QB.
.
:35 left first down. Chargers down by 3. They made the first down with an inbounds play so the game clock is running. Rivers spikes the ball to stop the clock.
.
That’s wrong. You only spike the ball when you do not have enough time to use your remaining downs. For example, if you have first down with :12 left and the game clock running, you spike the ball to stop the clock because you have four downs and :12 is only enough to run two plays.
.
In the event, The Chargers were unable to gain a first down on second and third down so they were forced to try a field goal from 45 yards. They missed and thereby lost the game.
.
Would they have gotten the first down if they had not wasted the first down with a spike? Maybe. Their chances would have been better with three downs instead of just two before they needed to kick.
.
http://www.johntreed.com/…/football-clock-management-5th-ed…
.

Here is the play-by-play:
.
1-10-CLE 35
(:44) (No Huddle) 17-P.Rivers spiked the ball to stop the clock.
2-10-CLE 35
(:43) (Shotgun) 17-P.Rivers FUMBLES (Aborted) at CLE 38, and recovers at CLE 38. 17-P.Rivers to CLE 38 for no gain (51-J.Collins).
3-13-CLE 38
(:28) 17-P.Rivers pass short left to 85-A.Gates to CLE 27 for 11 yards (21-J.Taylor).
4-2-CLE 27
(:00) 2-J.Lambo 45 yard field goal is No Good, Wide Right, Center-47-M.Windt, Holder-10-K.Clemens.
.
My book has my clock management rules. Rivers violated a hurry-up rule—Rule 4.00(o) which says: “Spike the ball only to stop the clock for a field goal when you have no timeouts left or when your number of downs exceeds the number of plays you can run in the half; do not attempt to spike the ball if fewer than :03 remain on the game clock at the snap.”