I know I'd personally rather spend more and not get cancer (as long as the tests aren't so invasive and unpleasant that they drastically lower the quality of my life), for example, than wait and treat the cancer later simply because that's the cheaper route.
This statement doesn't say that it's a bad idea, or that it shouldn't be done, or anything like that. What the statement does explicitly say is:
"Of course, just because a preventive service adds to total spending does not mean that it is a bad investment. Experts have concluded that a large fraction of preventive care adds to spending but should be deemed “cost-effective,” meaning that it provides clinical benefits that justify those added costs."
So, not necessarily a "bad thing". Just not something that can be honestly scored as saving money. Further conclusions are still up to you.
Please note that I am not commenting on the truthfulness or accuracy of this statement at this time, just clarifying the original message, to the best of my ability in my capacity as "someone who did not write it". Understanding what people are actually saying without politicized distortion (for whatever reason) is a necessary, but not sufficient, step to understanding the relevant issues.
So you are left with a question of allocation and rationing (no matter if it's government or private market rationing). So you need to figure the most cost effective ways of administering health across the population. Ethics falls into this as well, but is weighed against cost. (see Britain's drug board approving end-of-life drugs that add only a few weeks to life at large expense -- NY Times had something about it)
Basically, the flaw in your argument is that there's a presumption that there is infinite supply, and it just costs money to get at, so more money thrown at the problem (ie. more tests, prevention) means more treatment. But it doesn't work that way, it's a tradeoff. The doctor testing you for cancer today is not treating somebody who actually has it today. (simplistic, yes, but you get the point).