Are prophets' body decayed in their graves?

I heard a hadith that the bodies of the prophets do not decay; they stay unscratched in their grave. If this is true, does this mean that if we were to (aoozobillah) dig the body of Prophet Muhammad (pbuh) it would not have any decaying signs on it, and if it does this prove that Islam is false? Thank you.

Dear Brother / Sister,

Abu’d Darda reported:
The Messenger of Allah (peace be upon him) stated the following: “Recite a lot of ‘salawat’ (a prayer in which God is asked to bless the Prophet Muhammad and his descendants) on Fridays. The salawat recited that day are witnessed; angels witness them. Whoever recites a salawat for me, I am informed of it before its recitation finishes.”  
Thereupon, I said: “Even after you have died?”
“Yes, he said, even after I have died. For this reason, Allah, the All-Mighty forbade the earth to decay the bodies of the prophets. The Prophets of Allah are always alive, and they are blessed with sustenance.” (see Abu Dawud, salat, 207; Nasai, Jumua 5, 45; Ibn Majah, Janaiz 65; Ahmad b. Hanbal, IV, 8)
After explaining the virtues of the day of Friday, Hazrat Prophet (pbuh) advised his Ummah (Community) to recite a lot of salawat on that day in order that they could benefit from those virtues. And he said that these salawat would be reported to him. Thereupon, sahabas (the Companions of Our Prophet) found that information strange when they first heard it and they asked Our Prophet (pbuh) how these salawat would be reported to him “after decaying and disappearing,”.   
Hazrat Prophet (pbuh) answered the question that his Companions asked in surprise as follows:
“The earth is unable to decay the bodies of the prophets.”
So, this shows that prophets are alive in their graves. Certainly, this is an exceptional occasion which is within Allah’s power. And Hazrat Prophet reported it as mentioned above. Therefore, the believers believe it so. As it is narrated with an assumption proof, denying it does not necessitate kufr (unbelief) but denying it does not gain a person anything and deprives him from many things. (see al-Manhal, IV, 186-187; Sunan-i Abu Dawud Tarjama and Sharh, Shamil Publications, 4/126-127)  

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