There are many discussions of this on the web (Google: "Top Gear" source Nile), but I think the one on Reddit covers the main points solidly. In short, the "Top Gear" team redefined the phrase "source of the Nile" by first redefining "Nile" to include the Mediterranean Sea, thus moving the mouth of the Nile from Egypt to the Strait of Gibraltar. That resulted in the new source being in a location one could drive to (unlike the source recognized by everyone else).
So, no, they didn't, unless you want to use some very non-standard geographical definitions.
(By the way, most people agree Lake Victoria isn't the source since it has many feeders; the question is which of those starts furthest from the Nile's mouth.)