Broadband amps will amplify everything within their passband but they will not increase the noise level relative to local signals like X-10 RF so they are almost always an improvement. Most of the noise is just white noise - it's not other signals. As for noise being interpreted as an X-10 signal, that's extremely unlikely. The tuning of the receiver rejects out-of-band signals. I've done extensive testing (and, while I never made use of it and have forgotten more than I remember, 50+ years ago I knew enough about this to have an FCC license) and have only seen one very wideband and very inexpensive superregenerative Chinese made receiver that tended to be overwhelmed by the amplified signal, but the result was lost signals not misinterpreted ones. Multiple superregenerative receivers in close proximity can interfere with each other but, again, the result is lost signals not ones spontaneously created out of the noise. I've never seen an X-10 signal that I (or something like an X-10 security device) had not sent and I have never managed to capture an RF collision between multiple X-10 RF sources.
How do you think the much, much, much, much, much weaker signals from satellites like those that have left our solar system are received? It's because of good antennas and lots of amplification.
There are design flaws in X-10 PLC switches and modules that will allow brownouts and spikes to cause unintended ONs which are frequently misinterpreted by observers.