The DOL joint employment guide helps test whether two entities are both actually employers. Such as a case when a nanny works for both an agency and a home owner. It doesn't address a nanny share because, under joint employment law its completely obvious and without question that the employers in a nanny share are both joint employers. You don't need a special test for that. Just read the actual law:
Joint employment exists
a) Where two or more businesses exercise some control over the work or working conditions of the employee, the businesses may be joint employers under FMLA. Joint employers may be separate and distinct entities with separate owners, managers, and facilities. Where the employee performs work which simultaneously benefits two or more employers, or works for two or more employers at different times during the workweek, a joint employment relationship generally will be considered to exist in situations such as:
(1) Where there is an arrangement between employers to share an employee's services or to interchange employees;
(2) Where one employer acts directly or indirectly in the interest of the other employer in relation to the employee; or,
(3) Where the employers are not completely disassociated with respect to the employee's employment and may be deemed to share control of the employee, directly or indirectly, because one employer controls, is controlled by, or is under common control with the other employer.
The "tests" are from cases in which the employers were trying to argues that they were separate employers, or one was not an employer at all. The only reason I can think that a nanny tax service might not be 100% clear on this is if thy are extremely ignorant of the law, or, if they are considering cases in which a nanny truly has two part time jobs that never overlap in terms of benefits, location, or time
Arguing that the two employers in a nanny share might possibly be separate employers makes absolutely no sense. It would mean that the employers didn't have to coordinate vacation, for example. Which makes zero practical sense. It would mean that the employers could have different PTO policies. It would mean that if one employer stopped paying, the nanny would have to work for half pay unless she gave notice. It would mean that if the nanny worked for both parents less than 40 hours, but totaled more than 40 hours, she is owed no overtime. (Like if both parents were late on separate days)