I'd say that's the likely scenario. 4-way passive splitters are available, but not very common in the domestic field because of the losses involved in such a 4-way split of the signal. If the unit has an integral amplifier, then it must be getting power from somewhere: Some connect directly to the supply, others are designed to have power fed to them along one of the outputs to enable them to be fitted in places where power is not easily accessible.Now, if that is what the question was, then the small box they have disconnected was probably the power supply for the amp and not a single set amp.
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