The Rwandan government, or at least individuals involved with the Rwandan government at the highest levels, were making the broadcasts.

If anything they would have cracked down on opposing broadcasts by claiming that, since Tutsis are the historically privileged beneficiaries of colonialism who were collectively responsible for the violent oppression of Hutus, any pro-Tutsi or anti-anti-Tutsi sentiment was unconscionable hate speech while any pro-Hutu or anti-Tutsi bigotry was not technically racism. The power to ban “hate speech” is the power to define “hate speech” and hateful people will use against you the very same weapons you propose to fight them with.