I recently made the transition from full-time software engineer at bigco to independent consultant, so maybe I can help explain.
There's a fairly large mentality shift between salary work and contract work. When you're salaried, you're supposed to work eight hours yes - on paper. Really it's generally accepted people work 4-6 hours a day, with the rest being filled with lunch break or internet browsing or doing online chores or whatever. There is a tacit understanding between employer and employee about this, so any steps by the employer to monitor daytime computer usage is understandably seen as breaching this understanding in a misguided attempt to get employees to work more hours - or exposing the employee to arbitrary punishment if management wants to selectively undermine them for breaking rules that everyone breaks.
It's different when you're contracted per hour. When you carve out an hour for a client, it's game time. No faffing around on Facebook, no checking financial statements. You do the work. Does this mean you have to work a full 8 hours? Absolutely not. Just do part-time contracts to fill up as many hours as you want to work, then charge more per hour. Your hourly contract rate will be much more (2x or more) your hourly salaried rate anyway. So, since you're actually factually working during the contracted hours, I don't really mind whatever desktop screenshot system they want to use.
On another note: actually working 40 hours a week basically sucks. Let's acknowledge how good a deal we have as full-time tech employees and show solidarity to our brothers & sisters who do full-time shift work. Pushing full-time work down to 32 hours a week or less is a very worthy goal.