And why is it surprising to you?
You can read about how coefficients and their SE are calculated in linear regression. Standardized IVs have 0 mean and variance of 1. One component of SE(β) is inv(X*X'), where X is your design matrix, more precisely:
se = sqrt(model.MSE.*diag(inv(X*X')));
So: . We also know IVs have variance of 1, so , so we can simplify this to , which only depdends on IVs length.