I think it is not necessarily true that many redpacks => many injuries. Probably it is true during period with high injury rate. But after the cycle moved to next stage or the pattern of team operation changes, the statement may not be applicable.
A few seasons ago, my now level 15 team suffered severe injury problem and lack of red packs. However, after a season that I paid less time to manage (so using less red packs) and another season that my team only handle 1 league matches per day in most of the season (so I can rotate players without healing the starting players), my red pack balance gradually increased. It peaked at about 190 and now still have 164 after a wave of injuries.