While Mass Spec isn't necessarily the greatest in nondestructive sampling (if you have a cheap instrument that's only a few ten thousand dollars), there are forms of Mass Spec ionization chambers that involve soft ionization, which is less destructive sampling, so it's not so bad now! :)
For example, Matrix-Assisted Laser Desorption Ionization (MALDI) involves a sample matrix that basically absorbs a laser ionization source, and acts as an intermediate body between the laser and the atoms, and after the matrix gets ionized, it ionizes the atoms. That's an indirect, soft ionization, which fragments less, allowing easier observation of the parent peak(s).
What Robb G. was referring to was Electron Impact Mass Spec, specifically (although Electron Ionization is more accurate, because there is no actual collision), and that's not favored as much anymore.
There are much better Mass Spec ionization chamber variations, like CI and ESI, and there are other kinds of Mass Specs that ARE nondestructive, like Fourier Transform Ion Cyclotron Resonance (FTICR), Time-of-Flight (TOF) spectrometers, and Orbitraps, but they are on the more expensive end of mass analysis instrumentation out there (on the order of $800000~$2000000 for FTICR spectrometers).