How do we know?
This means 35 tests were positive.
Let's take essentially the worst case scenario that all 35 were false positives.
The specificity is TN/(TN+FP).
This means specificity = 949/(949+35) = 96.4%
But to save you time it is 95.1% - 97.5%
And that assumes nobody in nearly 1000 people had the antibodies.
But it is very likely another 1-2% will seroconvert because of this. More if the samples were collected a while back.
There is only one avenue wherein it could be massively wrong.
That is if they sampling somehow strongly enriched for people who were symptomatic.
In some high prevalence areas, the people who got a CLINICAL test had ~50% rate of having COVID19. So half of these high risk people with symptoms had other causes (viruses, allergies, etc.)
Seems quite implausible to me.
That could happen, but seems implausible.