I do not believe this is accurate. The Church teaches that anyone in a state of mortal sin cannot be saved, and that original sin is enough to preclude someone from Heaven, but it does not teach that everyone who is unbaptized will be denied Heaven. We hold out hope for those who are innocent apart from original sin. (Which is not itself sin, but rather an absence of saving grace.) Given that the grace of salvation is a gift freely given by God, commuted to us through the cleanings sacraments of Baptism and Confession, there is no reason that He would be unable to apply it to those people who were not able to receive baptism in life.
That being said, I personally believe that Limbo is probably as close to right as we’re going to get in this life. Jesus is pretty clear that baptism is necessary for salvation, but also that God is a loving father who desires the salvation of all. It doesn’t make sense to me that someone would be denied eternal happiness simply because they died before they were baptized, but I also have to take Jesus at His word. Limbo is the only proposition I’m aware of that satisfies all the criteria we’re aware of.