No, he's actually right (for the majority of apps).
For example, let's say you have two processors, both of which score 1000 on Geekbench, one with 4 cores, the other with two.
That puts their per-processor Geekbench score at approximately 250/core and 500/core. So, an app, which runs on a thread will run twice as fast on the dual-core chip than it will on the quad-core chip. (That's rough, because not all of the sub-benchmarks scale the same way between processors, but the base reasoning is sound.)
For an app which uses all available cores equally, the performance would be roughly equal on the two processors. If any given thread bogs down a core, it will slow down the overall performance of the application. Having faster individual cores helps mitigate this. Having more cores helps spread the workload of threads more evenly to minimize the odds that a particular set of threads will do so. It's a tradeoff, but for single threaded (or even lightly threaded) apps, faster cores are better than more cores.
