Assessing relative positional error in a DEM

I have a set of ground control points collected with a differential GPS and I am trying to assess the relative positional error (in contrast to absolute elevational error) in a DEM. I would like to know RMSE and standard deviation. My intuition tells me that I want to calculate all pairwise distances among ground control points and take the difference with the set of pairwise distances in the corresponding coordinates of the DEM as follows (in R):

set.seed(123)
pointNum <- 5

truth <- runif(pointNum, 70, 100) # my ground control points, elevation varying form 70 to 100m

noise <- rnorm(pointNum, 0, sd = 1) # make some noise with SD of 1

dem <- truth + noise # add the noise to simulate DEM with erros

distTruth <- as.dist(outer(truth, truth, `-`)) # calc the distance (raw difference) matrix between all control points
distDEM <- as.dist(outer(dem, dem, `-`)) # do the same for my dem 

RMSE <- sqrt(mean((distTruth - distDEM)^2)) # root mean squared error between the matrices
SD <- sd(distTruth - distDEM) # standard deviation between the matrices

Is this the correct way for calculating relative positional error?