In the unverifiable anecdote, it is claimed the Pope said "you are doing the work that we should be doing" (a statement that would be entirely uncharacteristic of Ratzinger). Note the similar tone in JW publications offering the same types of unverifiable anecdotes:
The Watchtower, 15 June 1993, page 26:
Upon
learning the purpose of their visit, the priest invited them in, and
they had a fine discussion. The priest then said: âI envy you but not in
a bad way. We should be doing the work that you are doing. Itâs too bad that the Orthodox Church is a sleeping giantâ!
The Watchtower, 1 January 1997, page 12 (recycled from Awake!, 8 February 1982, page 10 below, and also recycled in The Watchtower, May 2016, page 12):
WHILE preaching from house to house, one of Jehovahâs Witnesses met a Pentecostal lady who commented, âWe have holy spirit, but you are the ones doing the work.â
Awake!, 8 February 1982, page 10:
A pastor of a Pentecostal church once said to a Witness: âIt makes me cry when I think that we have Godâs spirit, but you people are doing the work!â
So even if the claim of being a first cousin (later revised to second cousin) were true (though it remains unverified and implausible given the absence of any Bergers in Ratzinger's family tree) and there was a phone call (which also remains unverified), it's still possible that the lady (who supposedly only reported the phone call 4 months later) mixed the details of the conversation with things she read in JW literature.