In fact, it is worth reading through to page 205, where this issue is discussed further and in some detail, with different positions explained. The change in the wording of the CCC is also mentioned.
I've been wanting to tend to this; it's only taken some 5 months!
The explanations, conjectures, for the change in the CCC are given there in the thesis as you state. This clarifies and is a rationale for the difference in wording of the CCC but it confirms, for me, that the Church is not wanting to discuss the matter in terms of minister or ministers of this Mystery/Sacrament. It is sidestepping this important issue and that is unfortunate. So, from the theses p 201-204:
The fact that sacred rite is an essential element of the canonical form of marriage brings up another difference between the Eastern and Latin traditions, namely the minister, or the ministers, of the sacrament of marriage.63 For the Latin tradition, the matrimony is a consensual contract which becomes a sacrament through the exchange of the consent between the two spouses.64 In fact the Catechism of the Catholic Church states: “According to the Latin tradition, the spouses as ministers of Christ's grace mutually confer upon each other the sacrament of Matrimony by expressing their consent before the church.”65 According to the doctrine of the non-Catholic Oriental churches the minister of the sacrament of marriage is the priest or the bishop who carries out the sacred rite through which the matrimonial sacrament is celebrated.66 Considering the minister of the sacrament of marriage, the Russian contemporary theologian Evdokimov affirms: “The priest is the minister of the sacrament that is instituted by God; mutual consent indicates that the betrothed are not bound by any other engagement, but the grace results only from the rite performed. In no way, nor in any sense, can the spouses be the ministers of the sacrament.”67
In the Catholic Oriental Churches there are two opinions concerning the ministers of the sacrament of marriage.68 One of them underlines the mystical and sacramental factor of the marriage and as a result considers the priest as the minister of the matrimony. The other opinion is closer to the Latin principle and regards the consent of the parties as the efficient cause of the marriage and consequently acknowledges the spouses as ministers of the matrimonial sacrament.69 In fact, this difference of opinions made its way in the process of preparation of the Catechism of the Catholic Church. Thus, the first edition of the Catechism of the Catholic Church stated that in the Oriental liturgies the minister of the sacrament was the priest or the bishop who, after receiving the mutual consent of the spouses, crowned them as a sign of the matrimonial covenant.70 Prader argued that this assertion referred only to the non-Catholic Oriental Churches.71 However, in the second edition there is no direct affirmation that the priest is the minister of the sacrament of marriage: “In the traditions of the Eastern churches, the priests (bishops or presbyters) are witnesses to the mutual consent given by the spouses, but for the validity of the sacrament their blessing is also necessary.”72 This change is significant because on one hand it underlines the value of the Oriental tradition by maintaining the necessity of the nuptial blessing, while on the other hand prevents the supposition that the sacrament of marriage has a different configuration in the Eastern Catholic Churches than it does in to the Latin Church.73
The two different opinions are indirectly present even in the current legislation. The CCEO does not specifically designate the minister of the sacrament of marriage but agrees with the 1983 CIC that consent constitutes the marriage.74 However, in order to remain faithful to the Oriental tradition CCEO stipulates in canon 828 § 1 that only those marriages are valid which are celebrated with the sacred rite in the presence of the competent priest or bishop. The second paragraph of the same canon explains that the sacred rite is carried out through the intervention of the priest who assists at and blesses the marriage.75
Take all that and add to it footnote 58, p200
58 Salachas, Il Sacramento del Matrimonio, 184. The Oriental concept that marriage is a sacrament conferred upon the parties through the priest‟s blessing brings out two other differences between Western and Latin traditions. First, in the Eastern tradition, marriage, as any sacrament, pertains to the eternal life in the Kingdom of God and cannot be dissolved by the death of the parties but creates between them an eternal bond, unlike the Latin belief where the matrimonial contract is dissolved by the death of one of the spouses. Second, in the Eastern tradition, marriage as a sacrament is a gift of grace. The parties might have made a mistake in asking the grace of marriage when they were not ready for it or they might show themselves unable to make this grace fructify. In these situations the Church may admit that in fact the grace was not received and consequently tolerate separation and allow remarriage. In opposition, in the Latin Church the matrimonial covenant has always been considered indissoluble. See Meyendorff, Marriage: An Orthodox Perspective, 54.
and this conclusion p 303-4
The conclusion of the second section of the first chapter was that until the eighteenth century there coexisted in the Eastern Byzantine Tradition two doctrines concerning marriage: one that considered consent as the fundamental element of the constitution of marriage and the other one which considered the blessing mandatory for the validity of marriage. It was not until the second half of the nineteenth century that the matrimonial doctrine underwent a significant change and the priestly nuptial benediction was considered to be the most important element of the sacrament of marriage.
and the comments of Fr. Deacon John and theophan, here, and the previous thread, and what emerges? I'm still not sure.
I say again that the Church, comprising East and West, needs desperately to resolve this issue starting
with a foundational theology of the Mysteries/Sacraments that informs the necessary canons rather than vice versa as seems to be our current situation.