It's possible to run "ssh user@server $command". This command does not write to bash history, as no shell is opened. I am wondering what signs are present on a server to show evidence of this command. I suppose at the time it is executing, it will be present in a ps output and maybe if you run "w" to see who is connected and what they are running? Otherwise, if you don't see the command whilst it is executing, is there any other information logged on the server about this? This is assuming you are running a command that isn't modifying files or somehow leaving traces of changes being committed.
Is there a unix utility that offers logging of such commands?
If what you need is actually an audit log then the bash history is not at all suitable anyway as that is removable/editable by the same user. (The bash history is essentially recorded for the benefit of that user so that they can reuse previous commands, etc.)
To get proper audit logging you would hook into the kernel with audit (on Linux, the same general idea would apply otherwise) and have it record the system events (command execution, file access, ...) that are relevant to your needs and store this log in a secure location (preferable on a different system entirely so that the audit logs are not lost in case of a compromised system).
Unless the respective user doesn't have a logging shell, such as sudosh (that, by default, also denies running commands like this), the commands that were ran will not be saved anywhere. You will be able to see in the logs (/var/log/secure usually) and in the last command that the respective users were logged in.