Yep. While the Terminal is not an option from the 4 apps listed in the initial screen, it's available from Utilities → Terminal at the top. They even provide a convenient way to access the hard drive from another computer: https://support.apple.com/guide/mac-help/macos-recovery-a-ma...
You're right that Terminal is accessible via Utilities, but Target Disk Mode and Terminal both require an admin password. Safari bypassed that authentication entirely, writing directly to protected system locations with no admin password