I tried to check the net. I couldn't find exact 3000 number, but the highest number I could find is that cotton bag must be used 7000 times. It varies according to the source though. If I remember correctly I read 3000 number for jute bag.
I also googled it and found multiple different results with numbers more like 100 times (which is quite easy to achieve in practice). I didn’t immediately find any results in the thousands, but isn’t looking for the highest number going to produce the statistically least likely outlier?
I think fixating on number of reuses to meet equal carbon footprint is fraught with problems and painting an incomplete picture though, this doesn’t really account for things like plastic production & waste toxicity, or the fact that plastic is non-renewable while cotton is renewable.
Source: https://phys.org/news/2018-08-reuse-bags.html . It has pdf linked of the Danish government study.