It's definitely true, and I'm surprised to see people saying otherwise. Stronger players ascend to higher ranks more quickly, leaving the others behind, so it only stands to reason that as time goes by the level of skill in a particular bracket goes down. It's not a dramatic change, but it definitely happens.
A rather extreme example to illustrate my point: Imagine playing against a rank 6 player on day 1 of the season. This is a guy who made rank 2 last season - a very solid player, within striking distance of legend, and in fact may have already made legend in the past. Now imagine queuing into a rank 6 player on the very last day of the season - this is (most likely) someone who has been fighting hard for the last several days to reach rank 5 but hasn't got there yet. They may not get there at all. The difference in skill between them and the guy in first example is likely pretty big.
The change is not hugely obvious day to day, but the skill level at any sub-legend rank definitely goes down as the season progresses.