This is not true. Here is data from my state:
The first chart shows the daily number of tests conducted (red), the cumulative number of tests conducted (blue), and the overall % of tests returned as positive (green), where it's just a simple calculation of cumulative positives over cumulative tests.
The second chart shows the rolling seven day average of positive tests.
You'll note in the first chart that early on the test positivity rate skyrocketed from about 5.5% to over 12% in the span of about a month. If you check the daily number of tests conducted, and keep in mind the log scale on the chart, you'll see that the testing capacity over that same timeframe approximately quadrupled. Also, on the second chart you can see average positivity went from close to zero average per day to about 180 average per day. So, during that month it is safe to say that increased testing capacity DID lead to more positives. That makes sense, at the beginning of the pandemic we had essentially zero testing and only severely ill people presenting at the ER were being tested and confirmed. During that month in question capacity ramped up, more people with weaker symptoms were being tested, and we learned that infection rates were considerably higher than initial indications.
From the peak cumulative positivity rate of over 12%, the rate plummeted back to about 5% in the span of 2 months. During those 2 months the daily number of tests conducted went up about eight-fold as capacity continued to increase. From the second chart the rolling average number of daily positives stayed relatively flat. Combine those three data points:
- Dramatically increased testing;
- Dramatically decreased cumulative positivity rate; and
- Flat average daily positivity rate
The, in mid-June cumulative positivity rate started going back up. Average daily positivity rate skyrocketed. But daily testing rate remained level or even decreased. What changed? Reopening. People got lax, the Governor's staff misinterpreted the cumulative positivity rate declines, and they made the unwise decision to relax restrictions. That's when the "first wave" REALLY hit. Today the cumulative positivity rate is as the prior peak (the chart is missing the most recent 5 or so days of data), average daily positivity rates are climbing again into a "second wave," and daily testing is down from the prior peak.
We're (the US) NOT having more tests come back positive because we're testing more. We're testing less! We're having more positive tests because people are idiots and overall we're doing a piss-poor job of managing the risk. We suck. We're not exceptional, except maybe exceptionally bad. Deal with it.