DHCPD logs show PC's requesting IP addresses from router when they are turned off. Are our log files incorrect?

Ask for the first question asked:

Is it possible that these computers could be turning themselves` …

Yes, computers can turn themselves on and have had this capability for ages. For IBM compatible PCs this is normal since they got ATX PSU's. (About since 1995). If you go to the motherboards firmware (aka BIOS or UEFI) you often have an option configure this. Quite useful if you have an old PC and want it to power up and boot before you get to the office.

The second part of your question

… and making themselves accessible to people outside of our network?

is independent from the first part. If that happens when the computers power on (regardless of whether they powered on by itself or by you pressing the power button) then you have a problem. If that is the case then the security breach has not been fixed yet.

Lastly, if you got the MAC address then you can look to the first three bytes. They will tell you which manufacturers made the network card that is requesting the IP. This can help to identify the source (e.g. only DHCP reqs from printers, or from mobile (personal?) phones…

I looked up the addresses in your post:

MAC addresses starting with F8:0F:41 or with 98:EE:CB belong to Wistron InfoComm. According to Wikipedia this firm makes tablets, mobile phones and other devices running the Chrome OS.

MAC addresses starting with 64:EB:8C belong to Seiko Epson Corporation. Those might be printers (then again, printers probably have their own IP range in an office, though possibly with a reserved MAC → IP on the DHCP server).

MAC addresses starting with 4C:A1:61 belong to Rain Bird Corporation. Every search I did on that name resulted in a sprinkler firm.

Finally:

Are our logfiles incorrect?

I doubt that. Somethings seem to be requesting IP information. This is being logged. No fault in the logging. The bigger problem is why are they doing that out of office hours? Is there a lawn sprinkler system which is powered on all day (and which is probably supposed to be on 24/7)? Are there printers which are not powered off but instead go to sleep mode? Are there laptops or PCs which do not get properly turned off but which instead go to a low power (sleep?) mode, detect low battery and power up in order to go to a deep sleep mode?

Basically, find out which device (should be easy, you got MACs and IPs, so you can either use documentation to look up which PCs it is, or use the router to find out which device it is). Then research further from that last devices. (In the case of a windows computer try powercfg lastwake).