Roman slaves were considered property, but they could in certain ways act legally on behalf of their master. If they did so, for example in running a business, the master was liable for the actions of the slave under his orders. This was also the case if the slave acted on his own. In that case however the master could free the slave, and then the slave would be held accountable himself.

I could not find any specific reference to murder, but I assume that in this case likewise the master would be held accountable for these actions. In times of civil wars, street fighting and murder could be part of political business and the Roman nobility used all assets it had, including slaves (which were sometimes freed for this purpose) and gladiators. They played a prominent role in attempts to steer elections of the public in a preferred way, but less so in the dealings of the nobility among themselves. The Roman nobility was, even in times of power struggle, uneasily bound to its institutions and code of honour. If they actually wanted to murder their opponents, they would try to do it themselves, or they would want a legal sanction of some kind to let it be done by state bodies such as the army.

For the specific time you are interested in: The planned murder of Cicero during the Catiline conspiracy was to be conducted by two Roman nobles, accompanied by other armed men. The attempt failed because Cicero had guards. In the later failed attempt at an uprising, the conspirators had also very clear ideas about which noble should personally kill opposing members of the nobility. Maybe, because they felt it was the right thing to do, maybe because they did not trust their clients and slaves to actually do it by themselves – the Senate had preemptively promised freedom and money for any slave who would give them information about the conspiracy. Still, their plan also included to raise slaves and citizens in revolt against the state. As the senate was aware of this, they send a praetor to Capua in order to put the apparently large body of Gladiators there under watch and to distribute them evenly into other Roman cities. Apparently they were afraid that the Gladiators might join the conspiracy and took measures to put them under control. For this story, you might want to read "Bellum Catilinae" from Sallust. It's an enjoyable, short read.

So, yes, what you are reading sounds believable, in a "it could have happened that way" kind of sense.