Three months before, maybe
From the article: "[...] the Earth had passed its closest in a very long while to the Sun just the day before."
Not exactly. The Moon's orbit precesses so that its perigee changes constantly. The Earth's orbit around the Sun precesses vastly more slowly, with its perihelion currently always in the first week of January.
On Jan 4th, 1912, these two events coincided to within 5 hours, a full Moon. There would have been much larger than normal spring tides around that date, possibly freeing grounded icebergs as the article stated. But, it's a reach to give this a major place in the circumstances of the Titanic's disaster.