I'm not entirely convinced by this. Not the bit about finding contemporary reports of old matches: I agree that's relatively simple if you've a mind and the energy to do it.
What I think I'd question is that reporters used the same standards for judging let-offs that we do today.
Today, we have endless slo-mo replays and Hawkeyes and stuff so it is relatively simple to say for definite that someone was let off or should not have been given out lbw. Without that technology available, it was generally accepted that the umpires were usually right, and mention was made of decisions in reports only when they were egregiously bad or close but crucial. Compared to the number of appeals and general discussions following replays we have today, disputed decisions were a rarity, really.
Fielding standards were lower, and I think there was a tendency not to categorise things as a chance unless the bloke actually dropped it rather than failed to make a fairly ordinary (by today's standards) leap to a ball a few feet away.
My basic point is that I think that spectators and commentators expected less of fielders in the old days, and were far more likely to defer to an experienced umpire's judgement calls as they had no access to technology which would allow them to challenge it.
That said, examining Bradman's figures, for instance, involves analysing a lot of matches played in the 1930s when pitches varied between shirtfronts and billiard tables and batsmen were never encouraged to take risks, so pottering along slowly and carefully to a hundred attracted very little criticism - whereas a batsman who now has the temerity to take more than a day to get a ton is accused of being desperately slow and of killing the game.
And I think that's going to be the key to understanding the variations in these stats over time: styles of play are very different now, with batsmen taking many more risks than they used to, and therefore being much more likely to offer chances. But if that's the case, then the inter-era comparison are going to be hopelessly off-beam: could a 1930s plodder deal with the way Test cricket is played today? How would a 21st century dasher cope with the sedate pace of pre-WW2 cricket?