The example you quoted about a woman who turned down a £7.50 p/h job in favour of living on benefits is probably more complicated than you think.
If you are in receipt of housing benefit, for example, there are thresholds for what you are 'allowed' to earn and still receive assistance with paying your rent.
Thus if you take a job for X no of hours per week earning X per hour, it is quite possible that your entitlement to housing benefit will drop drastically or vanish completely.
Of course, you still need to pay your rent; however the potential job at X per hour does not let you earn enough to pay that rent.
What are you supposed to do? Unless you are renting a property massively overpriced or above your actual needs (which you won't be, because HB barely covers average rent prices in most areas), if you took the job you would lose your home. You would be forced to move (you probably wouldn't be able to afford to do this, because moving between rented properties usually requires upfront payment of £1,000 plus) and/or downsize, probably to a home with fewer bedrooms than would be adequate, or to a place in a rough area, or far away from the job you were going for in the first place. This of course has knock-on effects eg would your kids have to move schools? How would it affect your partner's ability to travel to work?
It's not as easy as saying "Well she should take the job because it's better to be in work, sod everything else." We all have to live, we all need a roof over our heads. Rent prices are uncontrolled and astronomical across the country: I considered moving last year and couldn't afford to, because 2 bed properties in the area I was looking at started at £900 pcm. (And out of interest, a HB calculation for someone with entitlement to the full rate for a 2-bed property - ie not me - was around £800 pcm). I personally would only have been able to afford a studio flat or bedsit in that area, and I come with a DS.
Similarly, JSA: when you find a job you're interested in your advisor does a computerised 'better off' calculation. I did a ton of these when DS was younger and I was on IS. You spot a potential job, you think "Oh yeah, I could do that," and you take it up to the desk. The advisor does the sums and it turns out that you would be £30, £40, £50 per week worse off if you take the job, because of the ensuing adjustments to HB, tax credits etc. These are massive margins to people already on low incomes, to some it represents their entire food and utilities spending p/w.
This is what the benefit trap amounts to. It's not a matter of 'choosing' a life on benefits because you're lazy and feckless. It's because there are no other feasible options available.