Yes, most people say this, and Quark's attitude, not least as represented by its UK distributor, was very much as you describe in the 1990s. But InDesign did not kill Quark in the 1990s. Nor was InDesign 1.0 a breath of fresh air: it was a slow, syrupy arse of a program that was little better than a proof-of-concept.
InDesign only started getting into its stride with version 2.0, which only came out at the end of 2001. By this time, the management at Quark had changed and the company attitude towards users was completely switched.
In the year that Adobe launched Creative Suite (2003), QuarkXPress owners were being given printed manuals, quick-tip booklets (hell, I wrote some of these), video tutorials on CD, unlimited 24-hour hotline telephone support and free invitations to attend Quark conferences. The program itself had improved immensely since those dark days of the 1990s. You could create web sites with it, edit image files directly on the page, create multi-layout projects, roundtrip XML, and it was faster than InDesign, even if you were running an old non-Mac OS X version in an old Mac OS 9 environment. Even afterwards, Quark was updated to run natively on Intel Macs for nearly a year before InDesign got around to it.
The only absolutely essential feature that QuarkXPress lacked through the 2000s was a reliable PDF exporter. Quark tried to license PDF tech from Adobe, but guess what they said? Years later, once Adobe had utterly shafted Quark's attempts to keep up with an increasingly PDF-reliant prepress industry, it added insult to injury by releasing the code as Open Source.
When it came down to it, every Quark user would need a copy of Photoshop for their work. If they knew they could get Photoshop AND the rest of Creative Suite for the same price as a copy of QuarkXPress, they just bought CS, forgot about Quark and learnt InDesign instead.