I measured a high school course a couple of weekends ago and I pulled a steel tape over it.
I still think when you're measuring over an unpaved surface the wheel picks up irregularities in almost any surface that a runner won't necessarily have to deal with. Every irregularity, whether up or down, adds counts (or fractions thereof) to the wheel measurement, and those give you a longer length than you should get. The tape is largely immune to that.
I don't think deforming the surface is that big of a deal. For all practical purposes, the earth is the same diameter at the bottom of the deformation than at the top, and I can't imagine the surface is hard enough to deform your measurement instrument.