Can an outlet be installed at a splice?
Nope, because it's a receptacle in a bathroom

Any receptacle you add in any bathroom must be on a circuit that follows one of these rules.  


The circuit serves ONLY bathroom receptacles, and nothing else - no receptacles outside bathrooms, no fixed loads of any kind.  These bathroom receptacles can be in any number of bathrooms.  
The circuit serves ONLY loads in this bathroom - other receptacles here, light, fan, heat lamp, etc.   But every load this circuit serves must be in this bathroom.  


If the circumstances of this circuit qualify it for either one, then you can use it.  Otherwise, the advice you received is correct.