I cannot see how the narration is correct.
Kent was/is subordinate to Gloucester; the plight of any of that line would have no bearing on the line of succession in regard of the Gloucester issue.
Before William's birth, i.e. 17th Dec 1941, the line was:
{{{ Monarch's issue }}}
1 Elizabeth
2 Margaret
{{{ Monarch's sibling }}}
3 Henry, Duke of Gloucester (no issue)
{{{ Monarch's sibling }}}
4 George, Duke of Kent (2 issue - as below)
` 5 Edward of Kent (issue 1 of above)
` 6 Alexandra of Kent (issue 2 of above)
{{{ Monarch's sibling }}}
7 Mary, Princess Royal (2 issue - as below)
` 8 George Lascelles (issue 1 of above)
` 9 Gerald Lascelles (issue 2 of above)
etc.
At birth William of Gloucester would immediately displace the Kents and their subordinates. For him to be 5th would require issue of someone higher - King George VI, Princess Elizabeth or Princess Margaret.
Perhaps there is some confusion with his father Henry, Duke of Gloucester, born 5th in line ten months before the death of Queen Victoria.