No matter what is, or isn't presented, it will cause problems. It is in our nature to argue about stuff
I don't think it is unreasonable to present statistics. The problem is that statistics such as crash rates are presented as if they were risk, when in reality they are only a part of it, and the mental and physical health benefits, reduced pollution, and other things all contribute to the overal risk associated with cycling.
If risk were to be presented, including things like crash rates, people would pick it apart and argue about it. When crash rates are presented, people pick them apart and argue about it.
It is not reasonable to compare air travel to cycling because they serve different purposes. One can hardly take a commercial airliner to pick up milk, eggs, and the daily paper.
As for the historic data, the National Travel Survey began in the 1970s, so data collected before 1973(?) would have been collected by a different means, and may not be comparable. They also made some changes in the weighting methods in 1995. Details are available from the National Travel Survey Technical Reports.
That said, I doubt that it is very much worse in terms of quality, and I would look for other reasons for the low numbers. For example, was cycle modal share similar to now, but people just travelled that much less? People did not travel as far for work, school or shopping.
This report shows differences between 2005 and 2015, and there are significant differences for all modes. One of the things that I thought was most interesting was that the number of trips per person went down for all modes except cycling. At the same time, The distance per person went up for all modes except driving.
You also have to remember that active travel will be much more common in cities and towns, than across the population as a whole. There have also been significant shifts in where people live since the 70s. Populations have become more urban and less rural.
“In some ways, it is easier to be a dissident, for then one is without responsibility.”
― Nelson Mandela, Long Walk to Freedom