Answer: Yes, there is truth to it and yes you could kill the trees. I would suggest you consult with a professionally trained and certified arborist who cna inspect the trees and the site and try to determine a way to save them. There are some different methods that can be tried such as building a tree well with special air exchange pipes but they require special skill and experience to design. Oaks in particular are very sensitive to grade changes.
You might also want to consult with a landscape architect or engineer with professional training in drainage control and grading to make sure that adding soil is the way to solve that problem, too. Often, excess water such as runoff must be channelled away from a problem area and simply filling it in will not solve the problem because the water will back up somewhere else if it is not allowed to drain.
Good luck with the drainage and trees.
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