Originally, payroll companies did not need to be licensed. That is how the bulk of them operated. 100s of companies processed funds on behalf of their customers and no money transmitter licenses were required of them.
However, if we look at the flow of funds, if funds are processed through them, then yes, they are deemed to be money transmitters. As cited, In most cases, payroll companies worked with a licensed partner (like a bank) or a payment processor, but themselves did not have a money transmitter license. The payroll company handles all the information processing, whilst the licensed partner handles all the monetary processing. However, the money does touch their account which is where the problem lies.
If the payroll processor is not licensed, then arrangements must be made so that the payroll processor will never have access to your money. Only a licensed bank or MSB would have the legal right to accept funds from a company and process it for further distribution.
Recently 100s of payroll processing companies have gone into disarray because states like Texas, through their Department of Banking (DOB) have issued consent notices to cease operations to many payroll processing companies asking them to obtain money transmitter license in their state if they wish to do payroll processing, as per the definition of DOB/Texas, payroll processing companies are money services businesses and thus required to have money transmitter licenses.