Not sure why you had a bone to pick with these statements since they are widely advertised and well documented in reports from AAMC. Where did you see decade-range data that didn’t support these claims? When you look at tables that only show integer values for age it may seem like for a few years it was stagnant, but in actuality the decimal values were still increasing.
Most students enter college at 18 and graduate by 22, and gap year(s) mean that upon completion of undergraduate degree (typically 4 years) you did not begin medical school the following summer/fall (also beginning at 22). I also provide data from students directly responding if they took a gap year (and not just reliant on age) so that helps control for age anomalies. I’m only addressing matriculant data since that is more important for admissions than applicant data (we want to know the success stories, though from what I’ve seen applicant data also reflects all of the same trends shown below).
There used to be a better table AAMC provided with the trends over the last decade with decimal values, but I couldn’t find it (they often replace and move around data tables on their website). If anyone finds it please post!
Here it shows that mean and median age of matriculants (both men and women) is 24 and 23 respectively from the last two cohorts (which is 1-2 gap years): https://www.aamc.org/download/321468/data/factstable6.pdf
Data on page 6 shows that the average matriculant is more likely to be in the 23-25 (one or more gap years) age range than 20-22 (directly out of undergrad) and that this trend has increased just over the last three years. Question 16 reflects this trend when directly asked about gap years: https://www.aamc.org/download/419782/data/msq2014report.pdf
Here is the same report from 2012 to broaden the scope, and the same trends are continued (Question 17a also reflects this trend when directly asked about gap years): https://www.aamc.org/download/323378/data/msq2012report.pdf
Might as well show that GPA/MCAT scores increasing as well 2003-2014 for matriculants: https://www.aamc.org/download/321494/data/factstable17.pdf