This statement is generally true. Except for many small, but many times significant details.
Only a running up may consume CPU cycles. Period.
But an installed app may affect the system by changing its configuration. One example is DNS resolution. If you hit its configuration, you may notice considerable lags in many places in many apps. And there are more things like this.

Sheer volume of files stored on the disk may affect the directory seek times. Filesystem used by N900 does not use btrees for directory searching, so the factor is linear to the number of files in the directory.

And swap. This is not true, that swap eats CPU cycles. It does use CPU very little. But it is very I/O intensive. And app waiting for data from the disk is almost no different than app waiting for CPU - so the confusion.
But generally swap is a good thing, as long as your working set fits in memory. Swap allows to swipe unused or used very rarely apps, that are needed in background to have a complete system, out of memory and have more cells for the actuall used app working set.

A conclusion:
The sheer ammount of installed apps does not affect system responsivenes.
But an installed and not running app may affect system responsivenes by changing its configuration (ie resolver) and/or state (ie brings enormous number of files to the filesystem). But it is still a problem with particular app, not the exact number of apps.