First of all, I wonder: Do they think that people outside of their camps will accept their conversions? It all seems like an exercise in futility to me.
Now as for the actual halachic aspect:
In Toras Rabbeinu Shmuel Salant vol. 1 siman 29, R’ Shmuel Salant’s position is recorded as follows:
????? ?????? ???? ???? ?????? ????? ???? ????? ???? ?? ???? ????? ???? ?? ???? ????? ??????? ???? ????? ?? ????? ??? ????? ??”? ????? ?????? ????? ???? ???? ?????? ?? ????? ????? ???? ????? ????? ????? ??? ???? ?????? ?? ????? ?????? ??????? ????????? ??????? ???? ?????? ??”? ????? ?? ?????? ?????? ????? ?????? ???? ????? ??????? ????? ????? ????? ???? ?????? ????? ???? ??????? ????? ?????? ????? ??”?
But it doesn’t record the ???? which R’ Shmuel was responding to. However, in Shu”t Beis Avraham, we see that the ???? was sent by Rabbi Avraham Ever Hirschowitz to R’ Shmuel Salant and R’ Yaakov Reinowitz and both of their responses are printed there. The ???? was about a place where men are not allowed in the mikva and there are serious consequences and it would cause a Chilul Hashem if the dayanim go in.
You can see it here: http://www.hebrewbooks.org/pdfpager.aspx?req=59&st=&pgnum=55 (R’ Shmuel’s response is two pages later)
I would suspect that MK Lipman only saw the Toras Rabeinu Shmuel Salant and not the Beis Avraham, although it is possible to argue that the halachic reasoning would apply lechatchila. L’chal hapachos, R’ Hirschowitz, R’ Reinowitz, and R’ Salant all agreed that bedieved the geirus is good. R’ Ovadia and the Minchas Yitzchak also agree that bedieved it’s good. And perhaps lechatchila b’sha’as hadchak as R’ Ovadia writes: ??? ??? ???? ?????? ???.
The issue is applying this as a lechatchila in a non-sha’as hadchak. As far as I know, R’ Uziel is the only one to condone such a practice.
R’ Ovadia in ???? ???? ??? ? ???? ??? ???? ?? in fact has some choice words:
???? ??”? ???? ??? ????? ??????? (??? ?? ????? ???????) ??????? ??? ??? ???? ???? ????? ???? ?? ??? ????? ????? ??? ???? ????? ???? ?????? ?? ???? ???? ???? ??? ??? ????? (??? ????? ???? ???? ?? ????? ???? ????? ?????? ???? ???? ????? ?????? ???”? ??”? ?????? ??? ???? ???????? ???? ???? ?????? ?????? ?????? ???? ????? ????? ??? ????? ??????? ??? ????? ????? ??? ???? ???? ???? ???? ????? ???? ????)
He also says that R’ Shmuel Salant clearly was only mattir this in a sha’as hadchak.
However, I don’t see why they have to make such a big deal out of this. R’ Ovadia himself writes:
???? ?”? ????? ?????? ????? ????? ??? (????? ????? ??) ????? ???? ????? ????? ?????? ????? seemingly even lechatchila (although the Minchas Yitzchak says that it’s only bedieved and therefore suggests that the woman should tovel twice – once with this beged and with the Beis Din present, and once without the beged and with the Beis Din right outside listening). This would seem to address everyone’s concerns.
The Minchas Yitzchak can be seen here: http://www.hebrewbooks.org/pdfpager.aspx?req=14681&st=&pgnum=366 (and specifically ose 6 on the next page)