Bushmaster, those recorded miracles By Muhammad are from account witnesses just like how account witnesses recorded those mircales in the Bible.
However, there is something that needs to be understood here. As for every prophet who had miracles along his side and as we notice as we read though the bible and the Quran. Miracles in fact lead to people denying God's prophets more and more. It has happened on so many occasions, and if you notice the sequence in that, a punishment from God was followed for not believing even after the miracles. The case of Islam was different, all the prophet's mircales happened arounf the believers and that is only to strenghen their faith.When the prophet was carried to jerusalem and told them about it none of them believed. However he told them about the things he saw on his way there and explained in details on what spot he ascended to heavens. All of this proved to be right. When Khalifah Omar liberated Jerusalm, the exact spot was found as the prophet described. Many other mircales are also recorded, all the prophecies and such.