Two parts, and the first is a straight concession. The count is real and Christians should stop being surprised by it. It is what abundance produces: more copies means more variants, and a book preserved in three manuscripts would have a much prettier number and a much worse text.
The second part is where the objection is answerable. Ehrman's own textbook practice (he is a working text critic, not only a popular writer) is to weigh readings by manuscript age, geographical spread, and which reading better explains the origin of the others. Those are the ordinary tools, they work, and applying them is how we know which variants are trivial.
On the deliberate theological changes: he is right that some exist, and this page will not pretend otherwise. What is disputed is their weight. The changes he documents are mostly cases where a later scribe made an existing orthodox reading more explicit, which is a real phenomenon and a very different thing from inventing a doctrine.
And every one of the passages under discussion is printed in the apparatus of every critical edition, argued in public, and available to any reader who wants to check. A cover-up that publishes its own evidence is not much of a cover-up.