These ideas may be old news to most of us, but what many people will find more surprising is that the two statements look increasingly as though they're unrelated.
There's been a complete reassessment of these so-called antioxidant phytochemicals over the past decade and it now looks like they're good for us primarily in ways that have less to do with their antioxidant activity than we thought.
"Life used to be really simple," says Dr Roberta Re, nutrition research manager at Leatherhead Food Research. "Antioxidants mopped up free radicals and everyone was happy. Now it looks like it might be a case of bad branding, because the mechanisms involved are much more complicated than originally thought."
Take polyphenols and exercise, for example. Polyphenols are thought to support effective training, but how exactly are they doing it? The old idea was that they hoovered up the free radicals that accumulate in cells whenever we exert ourselves. But it turns out that the structures responsible for unlocking energy in cells mitochondria respond to oxidative stress by releasing their own antioxidants at levels that far outweigh the antioxidant effect delivered to cells by the phytochemicals from food. It's now believed polyphenols work instead by stimulating the mitochondria.
"We now know that the primary signal that primes the mitochondria to respond to oxidative stress is oxidative stress itself," says Dr David Stevenson, a researcher studying the health benefits of fruit in the Food and Wellness Group at Plant and Food Research in New Zealand.
"Oxidative stress operates through a signalling pathway in the cells to stimulate production of mitochondrial antioxidant enzymes and more mitochondria." More mitochondria means more capacity to generate energy for movement and, critically, less free radical production per amount of energy generated, he says.
"We don't know for sure how the polyphenols operate in detail, but it appears that they cause a mild oxidative stress so the mitochondria respond as if we were exercising. The benefits to health of polyphenols therefore appear to be the same as regular moderate exercise."
If they're right, this mechanism turns the idea of polyphenols helping because they're antioxidants on its head. "If anything, the antioxidant action of polyphenols would be expected to inhibit the adaptive processes by interfering with the free-radical signalling," says Stevenson.
This type of stimulation of natural cellular processes by phytochemicals is also the first of three separate mechanisms that seem to work together to protect our ageing brains, boost memory and stave off cardiovascular disease (CVD).
The second is the ability of polyphenols to increase the flow of blood and oxygen. "These compounds seem to increase the production of nitric oxide in the endothelial cells that line all our blood vessels. Nitric oxide is a major vasodilator so it protects against heart disease and strokes, as well as vascular dementia," says professor Jeremy Spencer, from the School of Food and Nutritional Sciences at the University of Reading.
Dr David Leake is also at Reading in the School of Biological Sciences, where he focuses on the role of flavonoids in CVD. He agrees that vasodilation looks increasingly likely to play an important role. "It may be affecting the diameter of blood vessels through increased nitric oxide activity in ways that aren't yet understood."
Polyphenols also fight inflammation throughout the body, and this is the third mechanism under scrutiny in both neurological and CVD studies.
"All these mechanisms are nothing to do with the antioxidant nature of these compounds," says Spencer. "They and their metabolites are acting like drugs, binding to receptors, stimulating signalling pathways and binding to immune cells. The one thing they don't appear to be doing is scavenging for free radicals in the body."
Leake agrees the antioxidant action of phytochemicals in the body has been overplayed: "They're metabolised, so you don't get much of the original compound. The small amounts you do get tend to be converted into metabolites that are not as good as the parent compounds."
Phytochemicals, then, appear to be at least as beneficial as we thought, but we're still working out why. This changing scientific landscape has not dampened consumer enthusiasm for plant-based antioxidants, according to Re. "Generally speaking we understand they're good for us, even if we don't fully understand why, so the market is still booming."
She says functional foods and drinks have a value of $19.4bn globally and the sale of antioxidants rose 8% from $350M in 2007 to $378M in 2010. More than 400 European product launches featured antioxidant claims between 2010 and 2011, according to Mintel.
Re also notes sales have largely been driven by increased demand for natural antioxidants and herbal extracts. Sales of synthetic products have remained virtually static. Green tea a rich source of the flavonoid epicatechin is a great example, exhibiting growth significantly greater than black tea, since 1997 according to Datamonitor.
However, the impact of Health and Nutrition Claims legislation across Europe has caused a major headache. The rules require manufacturers to back up health claims with scientific dossiers presented to the European Food Safety Authority (EFSA).
But EFSA is looking for a clear "cause and effect" relationship in controlled trials, which critics argue have more in common with pharmaceutical research than tracking the effects of changes in a normal, varied diet.
"At the end of the day, foods are not pharmaceutical agents," cautions Dr Lisa Ryan, deputy director of the Functional Food Centre at Oxford Brookes University. "You'd never want a food to have the same effect as a drug, but that's what they're looking for. It's very hard to harvest what nature has to offer in one molecule.
"Every compound has a different effect in the body and taken together you get cumulative, long-term benefits. My worry is there may be cases where we'll never be able to provide the evidence they're looking for."
"We can make links between things, like people who eat a lot of certain foods have lower levels of certain diseases, but if you want to say 'eat 10g of this compound and get this much benefit' then you often can't do it," agrees Re.
The permitted wording of claims may also prove obscure. The classic case would be EFSA's approval of a claim for the tomato extract lycopene that it "helps maintain normal platelet aggregation". Re doesn't think that'll mean much to consumers.
However, Spencer remains upbeat. "There's a huge amount of work going on and we're getting there. There have been well-controlled studies showing the benefit of cocoa flavonoids in CVD, for example." He predicts that orange juice and blueberries will be among the next foods to emerge successfully from the process.