Because there's nothing to gleam from the fact that she was summoned previously, infact in the Visual Novel she doesn't say that she was summoned in the previous War but was "summoned once before", she doesn't mention that she was in the previous Holy Grail War until later on the 4th day where she and Shirou talk to one another before going to be where Shirou finds out she made it to the war's finale and questions his worth as a Master to her (since within the first night Saber had been in 3 fights and was badly injured in 2)
Also, Rin mentions when Saber says she was summoned previously that it was quite rare. given what we know about the previous Wars with the exception of 3 no hero has been properly summoned twice under the Fuyuki System, the exceptions are
The Hassan-i-Sabbah, AKA Assassin, as all 19 leaders of the Hashshashin share the same name and the name of the sect is the etymological root of the word "assassin" with the class name itself thus acts as the catalyst to summon the members of the organization.
Type-Moon Wikia: Hassan-i-Sabbah
She isn't a clone of a Hero from the Throne of Heroes like every other Servant summoned
he was never unsummoned in the 4th war, Angra Mainyu's corruption unnaturally boosted his Independent Action Class Skill to the point he could stay in the world indefinitely
I am not including the Looped Holy Grail War which is featured in Fate/Hollow Atarxia as
is it a representation of the 3rd War with 5th war Servants acting as stand-ins for the Servants of the 3rd War and some Masters being based off from 3rd war, such as the Edelfelt sisters who look like Rin and Sakura
In Fate/Strange Fake Jack the Ripper is summoned as a Berserker for the False Holy Grail War in Snow Field and is a male (made sane by the Mad Enchantment Class Skill) but in Fate/Apocrypha Jack the Ripper is a young girl summoned as Assassin for the Black Faction.
Also, everyone who knew her identity she presumes had died as at the time she hadn't seen Kotomine nor know that Gilgamesh was still around and finally, given the normal procedure in the Holy Grail Wars to kill Masters to ensure they can't contract another Servant later on, with Gilgamesh being the only other Servant left to confront her she would assume Iskander and Waver are dead (however we know Waver is still alive)
As for your comment
Servants being summoned twice and retaining their memories was unheard of
Yes it's unheard of, mainly because every Hero summoned is not the real Hero but a clone as such they should not have memories of a previous war as the clone who has these memories is lost at the end. the bellow image and link explains it quite well
Soruce: Heroic Spirit - Accession
If this was not the case then Servants who become corrupted by the Grail particularly those in the Heaven's Feel Route would be corrupted in the Throne as well.
the Reason why Arturia isn't a clone is because she made a contract with the world prior her death to become a Heroic Spirit in exchnage for the Holy Grail, thus she wasn't summoned from the Thone of Heroes as the bllow image shows we however do not know what her corruption had done when she returned to her original time however if Fate/Hollow Ataraxia is any hope she is still her usual self just with a corrupt side to her as a second personality