I don't think this is accurate. Kimmel was relieved on the 17th, the day after TF 16 left Pearl. On the 21st Wake was hit by carrier based aircraft, alerting Pye that there was at least one carrier in the area. This was where Pye's resolve started to waver, he now considered this an evacuation operation instead of a reenforcement operation. This is somewhat ironic as this is exactly the situation Kimmel was hoping for when he organized the operation. But at this point, Fletcher's TF 16 was still 600 miles from Wake. Pye did decide to allow the Enterprise and Lexington groups to position themselves to aid Fletcher. I wasn't until after Commander Cunningham's "Issue in doubt" message the next day that Pye decided to recall the ships. Probably about the same time that our guys surrendered. It should be noted that while Wake was over-run, the Marines on Wilkes actually repelled the attack on that Island, however without any possibility of relief surrender was the only viable option.