No, that's not accurate.
The control rods had graphite tips, but were made of boron, which readily absorbs neutrons (graphite, not so much). One of several issues was that a bunch of the rods were completely withdrawn from the core. When the control rods were inserted, the first part in was the graphite tip. Graphite is a moderator, so it improved the efficiency of slowing neutrons down, making for an increased fission rate, which is exactly the opposite of what you want to happen when you are trying to shut the plant down. It was a design flaw, and was exacerbated by not following safety protocols - they pulled more rods out of the core than they were supposed to. The system also had a positive void coefficient, so when excess steam started forming inside the core, it increased the fission rate. Again, the opposite of what you want when trying to shut down.
It's not about the rods being cheap. There were design shortfalls and procedures were circumvented; multiple issues which all acted together to cause the accident.
https://www.vice.com/en/article/597k9x/why-the-chernobyl-nuclear-reactor-exploded
https://world-nuclear.org/information-library/safety-and-security/safety-of-plants/chernobyl-accident.aspx