@goofyfoot, it is definitely the opposite from what you were told. A larger object will not fit as far down into a 90 degree groove versus a smaller object of the same basic profile.
The degree to which they differ in their elevation on that groove wall can also be easily calculated. A 1mil (25.4 micron) diameter conical will ride about half way down a nominally cut unmodulated groove (50 micron width). A 0.6 mil (15.2 micron) conical will ride about 20% lower. That isn’t small change.
The contact area of both sizes are VERY similar. Why? Because the point of groove wall contact is on the spherical portion of the stylus. (Technically speaking, points of contact with a sphere are infinitely small but in practice you must consider groove deflection.)
Using a spheroid contact area is VERY important to allow for tolerance errors on the mounting of the stylus to the cantilever on the azimuth axis. This is also why fine line styli have a major radius. This is also why proper azimuth alignment has NOTHING to do with the stylus alignment in the groove regardless of stylus profile (up to a point, any way, but that point is usually past 2.5 degrees level headshell and often more)
Now, I would certainly argue that the smaller contact surface area of the stylus to the groove wall, the greater the chance for groove damage because the force is distributed over a smaller area, causing greater groove deformation. This is another advantage of fine line contact styli over conicals and also why a larger conical probably has a slight edge over smaller conicals in avoiding groove damage which is quite the opposite from what you’ve heard.
However, I AM ALWAYS OPEN TO NEW, YET CONFLICTING, INFORMATION. I invite it as it is the only way I’ve been able to help push this industry forward so far.