This doesn’t really tell the full story though.
Firstly, Pakistan’s “worst era” did not start from 2004 - our ODI team uptill 2006-2007 was pretty competitive. In fact, we were ranked number two in ODIs in 2006.
Indian cricket was certainly on the rise at that point, but they hadn’t really leapfrogged Pakistan until the likes of Inzamam, MoYo, Razzaq, Akhtar, Malik (pre 2008 version) etc. retired/declined.
India peaked in ODIs during the 2008-2011 period, and we didn’t play them in that period.
The 2012-2013 season was the perfect time to tour India - their stalwarts were in decline, and the young players had not fully come into their own at that point. England beat them in Tests, and we beat them in ODIs. They got rid of the deadwood after that series and became a top side again, starting with the Champions Trophy.
Since 2013, there have obviously been no bilateral series. So during Pakistan’s “worst era”, i.e. the 2010 era, the only time we faced them in a bilateral series was when India were in transition.
Hence, the qualification that India at their best have not been able to make inroads against Pakistan at their worst doesn’t hold true.
If Pakistan vs India would have played regular bilateral cricket over the last decade or so, there is no doubt that India would have closed the gap in H2H record somewhat.
From 2007 onwards, apart from maybe 2012, they have been consistently the better team over the last 10 years or so, and we have only played two bilateral series in this period.
Yes we beat a Dhoni-less India in the 2014 Asia Cup, but one-off wins can happen - however, I highly doubt that we would have been beaten them in a series in that time period. Quite a few would probably have been one sided affairs as well.