I found that generally, scientific studies do show a negative impact on phytochemicals like antioxidants, one such example stating:
An immediate decrease in the total antioxidant activity (23%) and total phenolic content (14%) was observed after addition of strawberry preparations to yoghurt. The total anthocyanin content did not change immediately, but decreased 24% throughout the yoghurt shelf-life. The individual compounds, (+)-catechin (60%), (-)-epicatechin (60%), kaempferol (33%) and quercetin-3-rutinoside (29%) decreased after 24h in the yoghurt made with the strawberry preparation. During the remaining period of storage these compounds increased by 47%, 6%, 4% and 18%, respectively. Pelargonidin-3-glucoside decreased 49% after 28 d. Immediately after the addition of the strawberry preparation to yoghurt, β-lactoglobulin decreased to values lower than the limit of detection and α-lactalbumin by approximately 34%, and was reduced further slowly throughout yoghurt self-life. An immediate interaction between the carrageenan present in the strawberry preparation and β-LG was observed. The variations of both polyphenols and protein in the presence of carrageenan and the potential interactions were discussed
As noted above, some phytochecmicals are available to the consumer longer than others in the presence of dairy. To be fair to the American Institute of Nutrition study referred to in the Nestle press release, they do not indicate for how long the antioxidants are still available after the introduction of dairy they only notate that after consumption they found coffee phenolics in the plasma of their test subjects:
Chlorogenic acids (CGA) are antioxidants found in coffee. They are becoming of interest for their health-promoting effects, but bioavailability in humans is not well understood. We hypothesized that adding whole milk or sugar and nondairy creamer to instant coffee might modulate the bioavailability of coffee phenolics. Nine healthy participants were asked to randomly drink, in a crossover design, instant coffee (Coffee); instant coffee and 10% whole milk (Milk); or instant coffee, sugar, and nondairy creamer already premixed (Sugar/NDC). All 3 treatments provided the same amount of total CGA (332 mg). Blood was collected for 12 h after ingestion and plasma samples treated using a liquid-liquid extraction method that included a full enzymatic cleavage to hydrolyze all CGA and conjugates into phenolic acid equivalents. Hence, we focused our liquid chromatography-Electrospray ionization-tandem MS detection and quantification on caffeic acid (CA), ferulic acid (FA), and isoferulic acid (iFA) equivalents. Compared with a regular black instant coffee, the addition of milk did not significantly alter the area under the curve (AUC), maximum plasma concentration (Cmax), or the time needed to reach Cmax (Tmax). The Cmax of CA and iFA were significantly lower and the Tmax of FA and iFA significantly longer for the Sugar/NDC group than for the Coffee group. However, the AUC did not significantly differ. As a conclusion, adding whole milk did not alter the overall bioavailability of coffee phenolic acids, whereas sugar and nondairy creamer affected the Tmax and Cmax but not the appearance of coffee phenolics in plasma.
Nestle press release found at www.nestle.com/media/newsandfeatures/good-news-milk-cream-coffee
Whichever line of research you choose to follow, it may not really impact your health over much anyway. The National Center for Complimentary and Integrated Health summarizes antioxidant research saying:
Several decades of dietary research findings suggested that consuming greater amounts of antioxidant-rich foods might help to protect against diseases. Because of these results, there has been a lot of research on antioxidant supplements. Rigorous trials of antioxidant supplements in large numbers of people have not found that high doses of antioxidant supplements prevent disease.
The NIH walks you through a lot of the findings at https://nccih.nih.gov/health/antioxidants/introduction.htm.