Yes, it is true. Xenon arc lamps (flash tubes) are a common light source used in accelerated aging tests, and will cause the breakdown of light-reactive (or "fugitive") pigments, as well as speed up the physical deterioration of paper, canvas and similar grounds. You can do a web search on the terms "accelerated aging pigment xenon" (without the quotes) to retrieve a number of scholarly papers on the subject, among them Pursuing the fugitive: direct measurement of light sensitivity with micro-fading tests (Whitmore) and Poly (vinyl acetate) paints in works of art: A photochemical approach. Part 1 (Ferreira et al).
(Most of the very recent work, admittedly, has involved pigments and binders for use in prosthetic devices -- nobody wants reverse tan lines on a very expensive artificial limb, or worse, on a facial prosthesis. The results still hold, but you'll have to page through results to find specifically art-related papers; archival testing of artists' materials is old science. See The Artist's Handbook of Materials and Techniques (Mayer, 1940; 5th edition 1991) for an extensive discussion of pigment, binder and ground lightfastness.)
No, your flash probably isn't going to do a whole lot of damage when you take a single picture. But think for a moment what you're doing when you take a flash picture: you're essentially throwing a substantial fraction of a second worth of sunlight (the quality of light -- that is, the distribution of the light's amplitude across the visible and near-visible spectrum -- is very similar) at your subject in the space of a millisecond. Now multiply that effect by hundreds or thousands of museum visitors every day for years on end. The museum might as well put the painting outside under the noonday sun.
Simply filtering out some frequencies, like UV and IR, won't help with the pigment destruction; those pigments tend to break down under the influence of visible light (it's what gives the pigments their colour and brilliance), though it does help to prevent damage to the support/ground and pigment binders (oils, resins and gums are more sensitive to UV and IR damage).