The heuristic should be don't rewrite the code base in businesses where time to market is critical and customer needs shift rapidly." Rewrites may make sense in markets where the competitive cycle time is long.
The point is sound. Except, as pointed out in Hacker News comments, when it's not.
My view is that Big Rewrites are always dangerous, but sometimes they're necessary. It's a very tricky decision, but either answer could be catastrophically wrong. So think very carefully about the specific circumstances from all perspectives: technical, business, competitive, political, functional, etc. You should certainly be biased against Big Rewrites, but you should also be aware that sometimes they work.
You should also seriously consider alternatives. For example, if you can do it, a skunkworks project (i.e. take a small team and assign them the task to build the cool new thing that will obsolete your main, problematic product) might be a better bet.