Since 1801 the Bagrations have been considered in Russia not as a non-reigning Royal House but as a bare aristocratic House; and in addition, the Bagration-Mukhransky branch was a collateral branch of the former Georgian Royal House, and that branch never reigned. Under this point of view, Bagration-Mukhransky Family had the very same status of other prominent Russian noble Houses, like Galitzine, Cheremetev, Chavchavadse, Yusupov, Golenishchev-Kutuzov, Vorontzov-Daschkov (and some of them had reigned over some Russian regions before Russia was unified).
The wives of several Romanov dynasts (in particular of Xenia Alexandrovna's sons) were born into some of the above listed noble Houses, but their marriages had been regarded as unequal.
Moving from the point that the Bagration-Mukhransky Family is equal to the other listed noble Houses:
A) if, like Grand Duke Vladimir declared, the Bagration-Mukhransky Family is equal to the Russian Imperial House, then also the other Houses are equal; so also the marriages of Xenia Alexandrovna's sons were equal and not morganatic. If this is true, then at Vladimir's death in 1992 Maria wasn't the only living dynast, but there were also male dynasts (Xenia's grandsons or the same Prince Nicholas Romanovic, whose mother was a Countess Cheremetev);
2) if all the above mentioned Houses, Bagration-Mukhransky included, are not equal to the Imperial House, then all the marriages of Romanov dynasts to members of these Houses are morganatic. As a consequence, nowadays there isn't anybody who can claim the Headship of the Imperial Family, because all the living Romanovs are descendants of morganatic marriages.
What Vladimir decided when he married to Leonida Bagration-Mukhransky was that the Bagration-Mukhransky Family is equal to the Imperial Family (despite in 1911 the marriage of a Princess of Russia to a Bagration-Mukhransky had been regarded by Nicholas II as morganatic); but at the same time all the other Houses had continued to be considered as unequal.