Yes, and it is one of the more frustrating realities of how prison administration works. The criminal standard of innocent until proven guilty does not apply to internal prison management decisions. The administration does not need formal charges or a conviction to place an inmate in higher security, transfer them to another facility, or hold them in the SHU. They need a documented reason to believe there is a security concern, and another inmate's accusation can qualify as that reason.
When one inmate accuses another of something serious, both are typically placed in the SHU while an investigation runs. The Special Investigations Services unit or an equivalent reviews the claim, interviews witnesses, examines evidence, and determines whether the accusation holds up. If the investigation finds nothing, the accused inmate is stepped back down and returned to the general population. If the investigation supports the claim, they can face disciplinary action, custody level changes, or in serious cases, criminal referral.
The interstate transfer element adds another layer. Transfers between states happen for a range of administrative reasons and do not require the inmate's consent or a new charge against them. Security concerns, real or perceived, are sufficient justification.
The inmate has the right to challenge administrative segregation through the facility's grievance process and, if necessary, through a civil rights attorney. Documenting everything from the beginning, what was said, when, and by whom, is the most important step while the investigation is ongoing.