Paul,
You place a back up at 1.44 for, say, £100. In the worst case scenario (which never used to happen, but with automation and these Indian kids working on it must be happening more now) this gets matched by someone who lays at 1.44 with 10,000 1 penny bets as you said. They can't lose (their liability is 0 because of the cumulative rounding error) and you can''t win since they are obviously on the other side of your bet. You would effectively end up backing at 1.0 (which in quirky fixed-odds pricing is actually 0).
What used to happen most of the time is that you would get hit by anywhere between 100 and 1000 of these tiny lays (depending on how liquid the market was). The end result being that instead of backing at 1.44 your effective price would be 1.40, etc. I'm sure you get the picture.
The reverse scenario doesnt work quite so well for them, i.e. them getting odds of 2.0 instead of 1.55 since their bet still has to win, otherwise they lose their stake. Done enough though it still works because of underlying principal of "value".
I think the amusing thing is that they feel compelled to state it was "an attractive young single mother". Would it be less interesting a story if it was a lass with a face like a spanked backside. It also strikes me as a not entirely productive use of a maths degree, but hey.