The ESD association sets the standards for removal of static in electronic manufacturing. 99% of the US manufacturers and 75% of electronic manufacturers world wide use ANSI/ESD S20.20-2007 (written by them)as THE gold standard. For more on their mission visit esda.org
The reason they recommend attachment to an electrical ground is the anti static mats have a very high level of electrical resistance. About 100 Meg Ohms. Enough to slow and control the rate of static discharge and for safety! It's virtually impossible for stray voltages to come thru them or an esd wrist strap.
Radiators rust, water pipes change potential. The only truly reliable ground is an electrical ground that has been (easily) tested. Attachment to the center screw of an AC face plate cover is standard industry accepted method of grounding your mat.
Incidentally all computers are manufactured in a static controlled environment. It's foolish to risk taking the chance with static. The manufacturers don't - for a very good reason - improper static control cost them money and aggravation.