First - AD accounts that end in $ are accounts that are created when a server or workstation is added to the domain. The name of the account is the same as the server name suffixed with $.

So, yes, network service is the likely reason. As for whether anything needs to be changed - well, that is entirely up to you and your organisation. It may be correct for the service to be using this account. Personally, I prefer to create specific accounts that can be given the minimum set of privileges for a particular function/application - this limits the potential for problems if there are any security breaches. This is the reason that you have proxies available within SQL Server Agent.