Much of the details of the mystical phenomena in the life of St. Joseph is recorded by eye-witnesses - sometimes several eye-witnesses. The events are also recorded in the documents for his canonizations. Many saints have had similar experiences - but perhaps the most well documented is that of St. Mary of Jesus Crucified, Discalced Carmelite of Bethlehem, who died in 1878 and was recently canonized. She too experienced ecstatic flight and ascensional ecstasy, well documented by her community and prioress, as well as workmen. Such phenomena is not a guarantee of sanctity, nor are Catholics obliged to believe it - so yes, one can take it with a pinch of salt - but that doesn't mean it is not true nor does it mean that it is not important for the edification of the faithful - in some cases, for the conversion of non-believers.
The Feast of the Stigmata of St. Francis, as well as the Feast of the Transverberation of St. Teresa of Avila are definite examples of how elevated and worthy of devotion these signal graces are for the edification of the faithful; to renew devotion, and to give glory to the Holy Trinity, among other things.
"One must see in it a divine or angelic intervention, which grants to the bodies of the saints an anticipation of the gift of agility which is proper to glorified bodies." - Benedict XIV
That said, articles by popular religious writers, devoid of actual theological understanding on such phenomena, tend to trivialize the charisma and do little to excite devotion, and in the process, they end up more or less conforming to modern revisionist theories downplaying the supernatural. All in all, Fr. L certainly affirms the supernatural aspect of the ecstasies of the Saint, and though he offers a slightly 'naive' reflection on his virtue and charismatic gifts, it seems to me a more reliable understanding of the phenomena would certainly complete Fr. L's article.
So what is ecstatic flight and levitation?
It's a quick search, a short read and easily found online - The Three Ages of the Interior Life:
By levitation is understood the phenomenon of the elevation of the human body above the ground without any apparent cause and in such a way that it remains in the air without any natural support. This phenomenon is also called ascensional ecstasy, ecstatic flight, or ecstatic walking when the body seems to run rapidly without touching the ground.
The Bollandists relate numerous cases of levitation. They cite particularly those attested in the lives of St. Joseph of Cupertino (September 18), St. Philip Neri (May 26), St. Peter of Alcantara (OctoBer 19), St. Francis Xavier (December 3), St. Stephen of Hungary (September 2), St. Paul of the Cross (April 28), and others. It is related that St. Joseph of Cupertino, seeing some workmen having trouble in trying to put up a very heavy mission cross, took his aerial flight, seized the cross, and without effort placed it in the hole destined for it.
In contradistinction to levitation, they cite cases of extraordinary weight of the bodies of certain saints: for example, when an attempt was made to violate and drag St. Lucy of Syracuse to a place of debauchery, her body remained fixed to the earth like the pillar of a church.
Suggestion or autosuggestion of hysterical persons has never been able to provoke levitation. After an examination extending over several years, Professor Janet of Paris was able to establish that the body of the person was never raised, even a millimeter, even sufficiently to slip a cigarette paper between his feet and the ground.(21)
Rationalists have tried to explain naturally the levitation proved in the case of several saints by the deep breathing of air into the lungs; but, in the face of the manifest insufficiency of this reason, they have had to have recourse to an unknown psychic power an explanation that is merely so many words.
Benedict XIV states the traditional and reasonable explanation.(22) He requires first of all that the fact be well proved in order to avoid all trickery. Then he shows: (I) that because of the law of gravity, well-proved levitation cannot be naturally explained; (2) that it does not, however, exceed the powers of angels and the devil, who can lift bodies up; (3) that consequently the physical, moral, and religious circumstances of the fact must be carefully examined to see whether there is not diabolical intervention; and that, when the circumstances are favorable, one can and must see in it a divine or angelic intervention, which grants to the bodies of the saints an anticipation of the gift of agility which is proper to glorified bodies. - Garrigou-Lagrange