What do you consider cheap? Last time I looked, injection molding machines were decidedly not cheap. Furthermore, the cost of a set of molds can run into the range of 6 to 7 figures.
(Aluminum or even SLA tooling is possible for smaller batches). That said, even good steel tooling does not necessarily cost above low 5 figures. It all depends on what you're trying to do.
Real injection molding machines are $10k-300k, depending on what you want / need. This is not very exciting or scary from a capital expenditure point of view. Yes, you can spend a lot more if you're producing a -lot-. That $200k machine can get you to thousands of shots per day.
Might be worth doing a test and order from your Chinese competitor to see how things look from your customers perspective.