The assertion is that there's roughly enough miners that miners make only a little profit. If your electricity costs $80 and you're likely to make $100, you're going to do it, and the OP is making an assumption that enough people have made that calculation that the amount of money made per miner is close to the cost of electricity per miner.

Therefore, the cost of electricity used should be close to the value of the bitcoins produced.

A new block gets mined every 10 minutes, each with a 25BTC bounty. That's 600 * 25 * 6 * 24 = $2,160,000 per day. No rational person would spend more in electricity than the reward, hence the 1-to-1 conversion. (In fact, miners do spend more than they earn, collectively.)

That's based on the idea that if bitcoin mining is profitable, more people will get in on it until it eventually becomes break even with the cost of doing it.

This is of course a big simplification, and neglects things like the upfront cost of building the mining equipment.