This is 100% true.
However, while you may never really drag yourself out of poverty you can certainly set your kids up for success. You may end up working an dead end job but you can move somewhere better and raise a family. With hard work and dedication (support from yourself and work from your kids), it is not impossible for your children to end up living a solid lifestyle from a professional career.
People are thinking too short term on this. If you are born in poverty you are much more likely to remain in poverty. However, your children can be very successful with hard work. You see this all the time with immigrants, who end up coming with almost nothing yet their children end up as engineers or doctors (etc.).
And this seems to be the problem. Doing this is not easy. It takes time and dedication and the majority of the results will never be reaped by yourself. Yet if you go back and look at everyone born in more fortunate circumstances, nearly all of them will have someone back in their ancestry who was self made from nothing (for instance a poor farmer's son who left home and moved to the city and eventually ended up a wealthy shopkeeper). Conversely, with many less fortunate people if you were to look back, you might (possibly) see someone who was much better off lose nearly everything (possibly through no fault on their part).
Poverty may not be something you might ever be able to get out of. However, with a lot of work, there is a good chance that you can get your kids out and end the cycle.