The "prophet" Muhammad stated that the angel Gabriel visited him with revelation and he put great importance upon Gabriel.
This is not true. Not if you are talking about the Koran, which never says this. This information comes from the Hadiths. If you were to base your understanding of Mohammed purely on his writings (i.e. the Koran) and not on the hearsay stories of later Muslim tradition, you would not come to the conclusion that Mohammed said anything about Gabriel.
The way Mohammed presents it in the Koran, it sounds like he's claiming Allah himself is speaking to him. There is no specific mention of Gabriel doing anything with revelation, other than in Sura 2:97-98 which is easy to miss. In fact, Michael is mentioned in the same context. Nowhere in the Koran does Mohammed specifically claim that any of his "revelation" comes from Gabriel. This specific place seems to be making Gabriel "confirm" the message (similarly to the Holy Spirit in Christianity) and that anyone who rejects revelation is an enemy of Gabriel and Michael and all the angels.
In point of fact, Sura 2:98 doesn't even specifically call Gabriel and Michael angels, but may even intend them to be human messengers, for it says "Whoever is the enemy of Allah and His angels and His messengers and Jibreel and Meekaeel, so surely Allah is the enemy of the unbelievers." It could even be taken that Gabriel and Michael are being placed in a third category all their own, and not among the angels nor the messengers. This would not be surprising considering the very low state of Mohammed's biblical knowledge (to be discussed below).
A reading of Mohammed's book (i.e. the Koran) will show that he pieced his "revelation" together from Bible stories that he heard taught (he obviously didn't read the Bible) and from stories and legends taken from the Talmud which he heard (e.g. the angels being commanded to worship Adam) and from Pagan stories which he heard (e.g. "God's own she-camel").
That he did not receive his information from any angel nor from actually reading the Bible is clear from how he mangles Bible stories, like getting Haman from the book of Esther into the story of Moses, and making Haman the builder of the tower of Babel, in Moses' day, by having Pharaoh say to Haman "Build me a tower so I can climb to heaven and see Moses' God." (Koran, in Sura 28:38 and Sura 40:36-37)
The Koran also confuses Mary the mother of Jesus with Miriam the sister of Moses, explicitly calling Mary "the daughter of Amram" (or Imram) and "sister of Aaron" several times. Its pretty clear that Mohammed has no sense of chronology, and thinks that Jesus was Moses' nephew and received the Injeel (Gospel) not long after Moses received the Tavrat (Torah), perhaps only a decade or so later.
This kind of mixing up of various biblical stories into one can only occur as a result of being illiterate, of not having read the Bible, and of accidentally mixing up stories you heard in your head. It would be hard to completely lack a sense of chronology if you had actually read the Bible. Surely nobody would mix up stories this badly on purpose. And surely no angel would be malevolent enough to play a dirty trick like this on anyone, or at least Gabriel would not.
Edit: In response to comments citing particular verses of the Koran which supposedly give Gabriel a more prominent place than I've suggested above. We must remember that the Koran is not like the Bible. You can't just translate the Koran with a formal-equivalence type translational methodology, because it will come out as ungrammatical jibberish. Muslims admit as much by teaching that "the Koran in untranslatable" and therefore they claim that to really read the Koran you must read it in Arabic. Contrary to this, the KJV translators write in their preface that even the "meanest" (i.e. roughest) translation of the Bible is still the word of God. The reason is we don't have to supplement a bunch of tradition and stuff from other sources to even end up with a grammatical sentence when translating the Bible. But with the Koran, you pretty much do. So without Islamic tradition and all the details that it adds about Gabriel and so on, it would be very hard to produce a translation of the Koran that's even barely readable. If you were, however, to attempt to wade through a literal, formal-equivalence, translation of the Koran, you would find all this stuff about Gabriel and several other things to be missing. This is another proof, in my estimation, that the Koran does not come from any kind of supernatural source, neither from God or any angel, nor from Satan or any demon, but merely from the mind of a man.