Well, you don't exactly sign in, at least in the conventional way, on an Android phone for a Google Account.
You have to use Settings, Google, and add any accounts you wish to use from the device there. It would be highly unusual for anyone to have any accounts other than their own on a given Android smartphone. These devices are considered to be single user devices and don't have multiple user accounts like PCs do that create entirely dedicated environments for multiple users. I have three Google Accounts and sync e-mail from all of them on my smartphone. It is quite possible to use multiple Google Accounts on a single smartphone, but within a single user environment. This presumes this single user should have access to all of those Google Accounts.
If you were to lose your phone you would most likely be using a tablet or PC to log in to your Google Account, not someone else's smartphone, and that's what they assume. I never accessed Android Lost from anything other than a PC when I needed to locate my phone which had gone MIA.
Brian AKA Bri the Tech Guy (my website address is in my profile) Windows 10 Home, 64-bit, Version 1709, Build 16299
Here is a test to find out whether your mission in life is complete. If you’re alive, it isn’t.
~ Lauren Bacall