Yes, a groundcover can be a spreading plant that covers the ground that may be too fleshy to walk on with bare feet but still they are plants that spread horizontally and are not tall shrubs.
Calling a thicket of spiny shrubs is really distorting the meaning of groundcover to the absurd no matter how anyone tries to justify it. A more appropriate term for their use would be hedge or living fence. Most popular horticultural references are flawed anyway and typically screw up out of ignorance when it comes to succulent and xerophytic plants and their uses.
None of the spinescent "Crown of Thorns" are horizontal growers. I should know, I have compiled a complete listing of all the species in the group that is Euphorbia subgenus Lacanthis.