"true and legitimate" is a correct and usable phrase in written English.
You can use it when talking about something being substantiated by facts or accepted as valid. For example, "The claim was true and legitimate, backed by evidence."
Ms. Hotchner fired back with a letter to the editor in Art in America: "Through our name change we hoped to change the public perception of the term 'craft,' so that we could use it in its true and legitimate sense.
"Jon Asgeir has a few times recently tried – in a tasteless manner in my opinion – to put pressure on journalists by complaining about true and legitimate stories concerning him … to the company's board and management," the letter said, though it insisted attempts to influence coverage had not been successful.
So it's both lawful and legitimate.
The country's debt and solvency are real and legitimate concerns, but the true crux of the friction lies in the implicit arguments about the cause of our troubles.
It belittles feminists' true legitimate and serious concerns - that the pay gap still exists, that violence against women is at crisis levels, that women's caring roles are so undervalued, that women are still woefully underrepresented in positions of power.
Withholding anticoagulant therapy seems appropriate and legitimate in the presence of true contraindications (eg, previous major bleed, thrombopenia, poor compliance).
Environmental Protection Agency Administrator Scott Pruitt made a similar request in an interview with Breitbart News, and demanded "a true, legitimate, peer-reviewed, objective, transparent discussion about CO2". Such calls for special teams of investigators are not about honest scientific debate.
This was true of both legitimate and illegitimate fertility rates.
That is true for legitimate purposes, such as detecting fraud, but in this case the agency itself may have crossed legal lines when it scooped up material submitted to or prepared for government agencies that investigate complaints from whistle-blowers, Congressional staff members and attorneys for the complaining scientists.
It's a separate and legitimate issue".
That's understandable and legitimate.
