You might be aware of this very useful service some 20 years ago, called 'Aalim Network'. I just came across a sunni website which referred to this article to prove that Hz. Omar married Hz. Ali a. and Hz. Fatemeh' (AS) daughter, Hz. Ume Kulsum.

The fact is that yes this article does say the following:
"Omar himself who married Ali and Fatemeh' (AS) daughter, Ume Kulsum. Secondly When Omar asked Imam's (AS) permission to marry her, Imam (AS) refused and said she is too young for marrying him. Omar swore " wa Allah-e I do not seek her for what you may think, I seek her because I heard the holy prophet (SA) saying 'get closer to me by being close to my family. I want to be closer to him by marrying his granddaughter." Whatever his true intentions were – perhaps a political gesture for the chilly political climate of the time when everybody knew that Ali (AS) did not let them to be present in the Salah to Fatemeh's (SA) body and her burial, or making confusion among the public and generation to come, or perhaps a call of conscience of guilt for what he has done to Fatemeh (SA)- Imam (AS) must have had good reasons for agreeing to the marriage."

Now, my question is that is this correct, and if it is, then why do Shias deny it?

In response to your question, I say:
The issue of the marriage of Caliph Omar to Um Kulthoum, daughter of Ali and Fatima ( peace be upon them), is very vague, as the news about it are conflicting, the stories received through the Sunnah say that the marriage took place, while the shiite narrations deny it, and while the first are weak, the second are considerable.
Some news also says that she is not Fatima's daughter, but ali's daughter from another wife, and some news says that she is the daughter of Abu Bakr, from Asma Bint Ommais, who was married to Ali (peace be upon him) after the death of Abu Bakr, and lived with her kids in Ali's house.
It is worth mentioning that the presence of a daughter of Zahra (peace be upon her) in the name of Um Kulthoum is not historically fixed, as a number of historians argue that Um Kulthoum is Zainab, and was called Um Kulthoum.
As it is well known, Zainab was has not been married to any one other than Abdullah bin Jaafar al-Tayyar.

On the other hand, The way they mention omar's marriage to Um Kulthoum, that Imam Ali (peace be upon him) sent her to him to look at her, and he hugged her, and revealed her leg, is a story that is not acceptable, because it is hurts the image and the dignity of Imam Ali (peace be upon him), and the position of the caliph. So from my point of view, this story has no fact behind it, but it is the story of the storyteller.
Allah knows the truth