I find it a bit hard to believe this story is true. I doubt any Catholic would have said such a thing before Vatican 2, let alone a religious. This sounds like modernist lies.
If you can find this story in a pamphlet or book about him written before Vatican 2, that contains an Imprimatur, I might give it some credence.
That December Karam recorded into the Center Log some of the statements he had heard Fr. Kelly make.
Among them:
It is possible for any man to be saved outside the Catholic
Church.
Any man who would say that there is no salvation outside
the Church is a heretic.
If you say that there is no salvation outside the Catholic
Church, you are a heretic and cannot save your soul.
The Catholic Church never defined or even suggested that
there is no salvation outside it. No pope, no council, no Doctor
of the Church ever taught that no one can be saved outside the
Catholic Church.
Not only is it possible to be saved outside the Catholic
Church, it is even possible to be saved while being an enemy of
the Church and actively fighting against it.
St. Paul was not sinning while persecuting Christ and
his Church.
The dogma that there is no salvation outside the Church
[this was said after Karam pointed out to Fr. Kelly that it was
a defined dogma] applies exclusively to Catholics who have
personally left the Church.
When a pope or council, or when a Doctor of the Church
says that there is no salvation outside the Catholic Church, the
meaning of this statement depends on what is meant by the
Catholic Church.
Baptism is not necessary for salvation.
Many people who are totally ignorant of Christ and His
Church can be saved because their ignorance excuses them and
confers on them baptism of desire.
A person can have baptism of desire, even if he is ignorant of
the baptism of water, even if he refuses to be baptized by water.
~Garry Potter,
After The Boston Heresy Case, pg.102
If Orestes Brownson and Fr. Michael Muller C.Ss.R needed to fight erroneous EENS interpretations +/-150 years ago it is not hard to believe that, by the mid-20th century, many Catholics held that anyone could be saved..even an atheist, as long as they were a "good person".
Ask any Novus Ordite if an atheist (or any other non-Catholic) can be saved and the answer will invariably be some form of "yes".
Ask any "trad" Catholic if a Jew, Hindu, Muslim, Protestant, etc. can be saved and the answer will, more often than one would like, be some form of "yes".
There are obviously degrees of EENS denial but this sort of thing does not happen overnight. I have read that Fr. Muller's writings on EENS (he does not deny BOD or BOB) came under fire from Catholics when he wrote them in the late 1800s
This is not to say I believe that Fr Casey said such a thing. I don't