Higher %s of false negatives as opposed to false positives doesn't necessarily lead to under-recording when the virus level is low because it is a higher % of a lower number.
If FNs are 10% and FPs are 1% of tests.
Test 100000 people randomly you should get around 100-200 positives at our recent levels. Say 100.
Of those 100, you end up getting only 90 positives because of the 10% rate of FNs so that under represents.
The other 99900, they will have mostly had correct negative results, but 999 will have had false positive results.
So whilst 100 had it, 1089 are identified.
NB. This is based on an illustration I read a month or so back from Heneghan. I'm not claiming it as my own work, but I've applied those figures to illustrate the problem.
Hope my maths are correct
It reminds me of a similar anomaly highlighted last Spring in the calculation of the R number where a total drop in numbers can be presented as an increase in R.