This is from the website of the SSPX. It seems to be an official statement.
My emphases and comments.
CONCERNING THE ULTIMATUM [They are calling it an "ultimatum" also.]
of Cardinal Castrillon Hoyos
Released on July 1, 2008 from DICI.
On June 4, 2008, at the request of Cardinal Dario Castrillon Hoyos, President of the Pontifical Commission Ecclesia Dei, the Superior General of the Society of St. Pius X, His Excellency Bernard Fellay, went to Rome accompanied the Second Assistant General, Fr. Alain-Marc Nely.
During the interview, he was given a memorandum in the form of an ultimatum, demanding an answer by the end of the month of June. On June 23, contrary to the established custom, [This is a subtle way of accusing someone working for the Holy See of having leaked the memo.] the Italian daily Il Giornale revealed the existence of the ultimatum and, the next day, published its content in its online edition. In the days following, the information was broadcasted by all of the international press. Thus, to the urgency of the ultimatum was added media pressure.
Cardinal Castrillon Hoyos’ document expressed five demands: besides  a positive answer requested before the end of June, the Society of St. Pius X, in the person of its General Superior, had to commit itself (1) “to give a response proportionate to the pope’s generosity”; (2) “to avoid any public comment which would not respect the person of the Holy Father and would have a negative impact upon ecclesial charity;” (3) “to avoid claiming a magisterium superior to the Holy Father’s and not to set the Society in opposition to the Church;” (4) “to demonstrate its will to act in all honesty and ecclesial charity, and in the respect of the authority of the Vicar of Christ.”
We must observe that the very general — not to say vague — [This is going to be a main point.] character of the demands singularly contrasts with the urgency of the ultimatum. [So, they are seeking to retrench by saying that the Conditions are "vague", and that they won’t be hurried to sign off on anything vague. They want concrete talks about issues.] The conditions seem to be meant to obtain an atmosphere favorable to a further dialogue, rather than imply any precise commitment on definite issues. The Society of St. Pius X wishes that the dialogue be on the doctrinal level and take into accounts all the issues, which, if they were evaded, [An slight hint that the Holy See is being evasive?] might jeopardize a canonical status hastily [There is the haste theme again.] set up. The SSPX considers that the preliminary withdrawal of the 1988 decrees of excommunication would foster serenity in the dialogue.
The SSPX does not claim the exercise of a magisterium superior to the Holy Father’s, [Condition 3. In a sense this fullfills that Condition. But we shall see in the future what they actually say.] nor does it seek to oppose the Church. Following in the footsteps of its founder, it wants to hand down what it has received, namely “what has always been believed everywhere and by all.” It claims as its own the profession of faith addressed by Archbishop Lefebvre to Paul VI on September 24, 1975: “Jesus Christ has entrusted to His Vicar the charge of confirming his brethren in the faith, and has asked him to make sure that every bishop faithfully keep the deposit of the faith, according to St. Paul’s recommendation to Timothy.”
In a letter to Pope Benedict XVI, dated June 26, 2008, Bishop Fellay answered in this sense. Cardinal Castrillon Hoyos acknowledged receipt of the letter the next day.
Until further details are available, we will make no comment.