The USBC rules allow it. Most leagues that I know of have no specific rule against it; therefore, it is allowed. Oddly, many bowlers seem to believe it is not allowed but bowlers are famous for not knowing their own rules.
Many tournaments, like USBC's own national tournament, have specific rules preventing anything but a dry towel (and the bowler's hand) from ever touching the ball. Since the USBC allows it, this tournament-specific rule seem to imply they don't think much of their own "official" rule.
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"...for advice is a dangerous gift, even from the wise to the wise...."
J. R. R. Tolkien