No second baptism takes place if the first is administered by heretics, and therefore is no baptism at all, but rather a pollution, as the Fathers say.
Which jurisdiction was your friend coming from when she was rebaptized?
The sacred Synod of ROCA under blessed Met. Philaret could also be accused of fanaticism using this same argument.
It's not a question of one method of reception being absolutely right and the other wrong, it's a question of a rigorist application of the canons vs. economia, which should be left to the bishops to decide.
RESOLUTION OF THE COUNCIL OF BISHOPS OF THE RUSSIAN ORTHODOX CHURCH ABROAD
15/28 September, 1971
On the question of the baptism of heretics who accept Orthodoxy the following resolution was passed:
The Holy Church has from old believed that there can be but one true baptism, namely that which is performed within her bosom: "One Lord, one faith, one baptism" (Eph. 4:5). In the Symbol of Faith "one baptism" is also confessed, while canon 46 of the holy apostles decrees: "we order any bishop, or presbyter, that has accepted any heretics' baptism, or sacrifice, to be deposed."
However, when the zeal of any of the heretics weakened in their battle with the Church, or when the question of their mass conversion to Orthodoxy arose, the Church, to facilitate their union, received them into her bosom through another form. In his first canon, which was incorporated into the decrees of the Sixth Ecumenical Council, St. Basil the Great indicates the existence of various practices in the reception of heretics in different countries. He explains that every separation from the Church deprives one of grace and writes concerning schismatics: "The beginning, true enough, of the separation resulted through a schism, but those who seceded from the Church had not the grace of Holy Spirit upon them; for the impartation thereof ceased with the interruption of the service. For although the ones who were the first to depart had been ordained by the fathers and with the impartation of their hands had obtained the gracious gift of the Spirit, yet after breaking away they became laymen, and had no authority either to baptize or to ordain anyone, nor could they impart the grace of the Spirit to others, after they themselves had forfeited it. Wherefore, they [the ancient partisans of Sts. Cyprian and Firmilian] bade that those baptized by them [the heretics] should be regarded as baptized by laymen, and that, when they came to join the Church, they should have to be repurified by the true baptism as prescribed by the Church". However, "for the sake of the edification of many," St. Basil does not object to the use of another form of reception for the schismatic Cathari in Asia. Concerning the Encratites he writes: "If, however, this is to become an obstacle in the general economy" [of the Church], another practice may be employed, explaining it in this way: "For I am inclined to suspect that we may, by the severity of the prescription actually prevent men from being saved. . ."
Thus, St. Basil the Great, and through his words the Ecumenical Council, while confirming the principle that outside the Holy Orthodox Church there is no true Baptism, allows through pastoral condescension the reception, called economy, of certain heretics and schismatics without a new baptism. In conformity with such a principle, the Ecumenical Councils permitted the reception of heretics in various ways, corresponding to the weakening of their embitterment against the Orthodox Church.
The Kormchaya Kniga (the Slavonic Rudder) cites an explanation of this by Timothy of Alexandria. To the question: "Why do we not baptize heretics who have converted to the Catholic Church?" he replies: "If this were not so, man would not readily turn away from heresy, being ashamed of baptism [i.e. a second baptism], knowing moreover that the Holy Spirit comes even through the laying-on of a priest's hands and through prayers, as the Acts of the Holy Apostles testify."
With regard to Roman Catholics and Protestants who claim to have preserved baptism as a mystery (e.g. the Lutherans), in Russia since the time of Peter I the practice has been followed of receiving them without baptism, through the renunciation of their heresy and by the chrismation of Protestants and unconfirmed Catholics. Until Peter's reign, Catholics were baptized in Russia. In Greece the practice also varied, but for the past almost 300 years after a certain interval, the practice of baptizing those converting from Catholicism and Protestantism was again introduced. Those received in another manner are not recognized as Orthodox in Greece. There have been many cases in which such members of our Russian Church have not been admitted to Holy Communion.
Having in mind this circumstance and the growth today of the heresy of ecumenism, which attempts to eradicate completely the distinction between Orthodoxy and all the heresies, so that the Moscow Patriarchate, in violation of the sacred canons, has even issued a resolution permitting Roman Catholics to receive Communion in certain cases, the Council of Bishops recognizes the necessity of introducing a stricter practice, i.e. that baptism be performed on all heretics who come to the Church, excepting only as the necessity arises and with the permission of the bishop, for reasons of economy or pastoral condescension, another practice of reception in the case of certain persons (i.e. the reception into the Church of Roman Catholics and those Protestants who perform their baptism in the name of the Holy Trinity) through the renunciation of their heresy and by chrismation.
Translated from: Orthodox Russia, Vol. 42, #20 (15/28 Nov., 1971), p. 12. This article and the resolution was published in Orthodox Life, Vol. 29, No. 2, 1979, pp. 35-43.