I've not seen the One Show for a while so I've no idea if you are correct.
However regarding the name of the flag
http://flagspot.net/flags/gb.html#nam
It is often stated that the Union Flag should only be described as the Union Jack when flown in the bows of a warship, but this is a relatively recent idea. From early in its life the Admiralty itself frequently referred to the flag as the Union Jack, whatever its use, and in 1902 an Admiralty Circular announced that Their Lordships had decided that either name could be used officially. Such use was given parliamentary approval in 1908 when it was stated that "the Union Jack should be regarded as the National flag".