Some would have us believe that God is present everywhere. It is not so. He is no more every where present in person than the Father and Son are one in person. 6:345.
In the Journal of Discourses, Brigham goes on to say that "The Bible teaches that doctrine precisely as it is." Interestingly, in the quotation following this one Brigham refers to a Bible verse (Psalm 139:7) which seems to teach pretty convincingly that God is present everywhere. I think that when Brigham says that the Bible teaches "that doctrine" precisely as it is, he means the doctrine that the Father and the Son are not one person. For details on that thought, see this quotation.