n0m, they are actually very much, as you put it, “controlled” in that regard.
Kolaiv davened by Kivrai haAvos “Avosai bikshu alai rachamim”
When visiting the Kever of their Rebbe Lubavitchers follow a specific proscribed customs (that they have for generations).
Among them, as relates to your comment, they include:
Beforehand they all {give extra Tzedaka for, and} write a “Pidyon Nefesh”, which follows the Nusach of “ana leorer rachamim rabim baavur so&so ben/bas so&so” followed by their Bakashos..
(The huge lobby on the way into the bh”k has seating, pens & paper to use for this..)
At the Kever, they all Daven from the ‘Sefer Maaneh Lashon’, during which there is a specific place/context:
יהי רצון מלפניך .. בזכות הצדיקים .. הנקברים פה .. יהיו עלי מיליצי יושר .. אמן סלה
where they read their P”N, before continuing to Daven in the Seder haTefilos.
See here: https://hebrewbooks.org/pdfpager.aspx?req=15693&pgnum=14
(At the Ohel/Kever there are shelves full of the M”L in Hebrew/Aramaic & English, and on top of the Kever there are the many P”N’s which were torn up and left once read).
For those who have limited time (or who are not particular with every one of the additional customs involved) at a minimum they have a P”N in the Nusach etc, and they daven from the M”L as much as possible (certainly at least to where the P”N is read), often continuing the M”L, after having left, until they’ve finished.
So far them, the Nusach of the M”L in conjunction with that of the P”N ensconce the context of their Tefilos very clearly.