First of all, Yasir Qadhi: https://www.youtube.com/watch?v=9Tsf29m9_O4

Transcribed part of what I took from:

And remember that marriage is a solution, so you should seriously consider it. The Prophet Lut 'alayhis salam told his people, “These are my daughters, they are more pure for you.” Some scholars say that when he said “daughters”, he is also implying the women of the town and not just his own daughters. So he's telling the men of his community who were guilty of this crime to go and marry women, for they are better and purer for them. Marriage is a solution, because sensuality and sexuality is something that can be satisfied – rather it should be satisfied – by the opposite gender within the confines of marriage.

So yea, it isn't just something made up. Read Quran 11:78, and see what a Prophet recommended for the people of Lot:

And his people came rushing towards him, and since aforetime they used to commit crimes (sodomy, etc.), he said: "O my people! Here are my daughters (i.e. the daughters of my nation), they are purer for you (if you marry them lawfully). So fear Allah and degrade me not as regards my guests! Is there not among you a single right-minded man?"

As for the fact that celibacy is haraam then I will show you (and I took from classes, not from these websites anyways): http://www.alifta.com/Search/ResultDetails.aspx?languagename=en&lang=en&view=result&fatwaNum=&FatwaNumID=&ID=4023&searchScope=14&SearchScopeLevels1=&SearchScopeLevels2=&highLight=1&SearchType=exact&SearchMoesar=false&bookID=&LeftVal=0&RightVal=0&simple=&SearchCriteria=allwords&PagePath=&siteSection=1&searchkeyword=099101108105098097099121#firstKeyWordFound