My friend's daughter can't remember her screen lock PIN.
I googled and found found how to get to the factory reset menu.
BUT, it also says that after factory reset, the phone will ask for a Google account, and she does not have one
Is there any way to totally factory reset without a Google account?
Related, for others with this problem, see this question. Personally, I am am afraid to try it, and it is not a Samsung device anyway, but that might help someone.
I think you misunderstand what it is saying here... It is referring to FRP (Factory Reset Protection) which is a method of protecting the phone from unauthorized access by third parties when it is factory reset by requiring you to log in to the Google account that was setup on the device prior to the factory reset.
Three outcomes are possible here...
There was no Google account setup on the device, a factory reset will clear all data and the phone will startup to the Setup Wizard like normal. FRP will not be a part of this situation. If there was no Google account on the device then you would not have been able to access the Play Store either, if your friend's daughter was able to access the Play Store then she had a Google account on the device.
There was a Google account setup on the device that is not known now and there is no way to recover it. If you factory reset at this time, the FRP will kick in on the first boot as part of the Setup Wizard and you will be required to enter the email address and password of the Google account that is not know. FRP will prevent any access to the device. In 99% of cases there is no way around this situation and the device will be permanently unusable.
There is a Google account setup on the device that is known. If you factory reset at this time, the FRP will kick in on first boot and you will enter the Google email address and password and FRP will be completed and turned off. The Setup Wizard will complete normally.
Unfortunately, we see more and more of #2 recently, and the device is basically a brick after a factory reset. A few specific models have a bypass for FRP, but those a few and far between and often require ADB and/or fastboot access to the device.
If this is an older device, prior to Lollipop (meaning Android 4.4 or older), then FRP is not an issue anyway since it is not incorporated into ROMs that old. Lollipop or higher is required for Google FRP.
Also, this is nothing new, in fact Google has been a bit behind in this are for a while... Apple's iOS and Microsoft's Windows Mobile operating systems have been doing this for some time now.
Q & A