There are two independent factors regarding the bandwidth of a signal: the frequency range of the audio fed to the modulator, and spurious distortion products.
The apparent bandwidth of a signal is the sum of the actual bandwidth plus the selectivity of the receiver. Many times, hams seem unaware of this; the ultimate example is the occasional SSB operator heard pissing 'n moaning about the "wide" AM carrier producing a squeal all the way across 3 kc/s of the band. A 6 kc/s wide AM signal will have an apparent bandwidth of about 9 kc/s of total dial space on a typical SSB receiver.
Don's very important point is missed by many of the complainers who understand a lot more about griping than they do about measurement. Those expensive highly selective filters aren't put into spectrum analyzers and frequency selective voltmeters just to take up space but are critical in attempts to measure the true bandwidth of a signal. Typical filters used in ham receivers and transceivers are relatively broad and have a less than perfect shape factor.