All Muslims are supposed to be one entity and one body, and all of them should cooperate with one another to the welfare and public interest of all. The hadith referred to in the question epitomizes a high form of social solidarity that should be a common feature in the Muslim society. The Prophet (peace and blessings be upon him) is reported to have said: “Never does charity cause wealth to diminish.”
Dr. Mahmoud `Abdullah Al-`Ekazi Prof. of Comparative Jurisprudence at Al-Azhar University, states: Social solidarity is one of the essential aspects of brotherhood, if not its most prominent aspect. By social solidarity, we mean the collective feeling of duty toward one another. It is also one of the laws of any developed community, and an element of the good virtuous life on which the happiness and noble existence of nations depend. Among the actions associated with social solidarity are giving a helping hand to society in various ways including aiding the grieved, relieving people during times of calamities, securing those who are afraid, satisfying the hungry, and contributing practically in the establishment of public interests. That is why we find the noble Qur’an and the purified Sunnah exhorting us to give in charity.

Almighty Allah says, “Take alms of their wealth, wherewith thou mayst purify them and mayst make them grow.” (At-Tawbah: 103)
The Almighty also says, “…and My mercy embraceth all things, therefore I shall ordain It for those who ward off (evil) and pay the poor due, and those who believe Our revelations.” (Al-A`raf: 156)
Furthermore, At-Tabarani reported a hadith that reads: “He who pays the zakah due on his property, its (the property’s) evil has gone away.” In another hadith, the Prophet (peace and blessings be upon him) says, “Perform prayers, pay zakah, perform Hajj and `Umrah, and be straight so that all your affairs may be straightened.”
In addition, Ibn Majah reported a hadith in which the Prophet (peace and blessings be upon him) said, “O people! Turn to Allah in repentance before you die; do good deeds before you get preoccupied; and strengthen that which is between you and your Lord by remembering Him most often and giving in charity most often in secret and in public so that you may be given provision, victory and support.”
The hadith mentioned by the questioner was reported by Abu Dawud as a hadith mursal (i.e. an incompletely transmitted hadith whose chain of transmitters lacks a Companion transmitter). Its exact wording is as follows: “Immunize your property with zakah, cure your ills with charity, and confront the waves of distress with invocation.” The same hadith was also reported from a group of Companions as a muttasil hadith (i.e. a hadith with a connected chain of transmission) and its meaning is clear.
The above hadith indicates that the charity giver who sincerely fears Allah is contained in the care and mercy of Allah. This is inferred from the first verse we mentioned and from the verses in which Almighty Allah says, “…And whosoever keepeth his duty to Allah, Allah will appoint a way out for him, And will provide for him from (a quarter) whence he hath no expectation.” (At-Talaq, 2-3) Therefore, charity purifies property and takes harm away from the charity giver.