Looking for source: Biologic reactions of people saying "no"
Most of the claims that &quot;saying no is good for one's health&quot; are grounded in psychology. In other words, they are  not experimentally verifiable. Likewise, health here refers not only literally to physical health, but also to psychological health, which in itself is something hard to define.
Surely, in situations of high stress saying &quot;no&quot; can actually result in some measurable responses, in which case it can be studied within the context physiology and neuroscience. However, this would address only a small part of the situationd covered by the original claim - discarding any effects on psychological health as well as long-lasting effects on the physical health.
To summarize: for a scientific study the claim needs to be made more specific, i.e., apply to well-defined situations and responses.
Disclaimer
I feel that a clarification is needed, lest what I wrote above is interpreted as a negative view of psychology.
I am not claiming that all of the psychology is outside of the scientific method, but a big part of it is - at least outside of being possible to study in a laboratory setting. And this is by no means unimportant part, in terms of the role it plays in our society. While words not scientific often carry negative connotation, in practice any scientist should recognize that scientific method has its limitations - many phenomena (psychological, social, economic, etc.) are not sufficiently reproducible and controllable to study experimentally, yet too important to dismiss.