Short answer, no.

Long answer, it's a variable you need to consider when doing data analysis, and it depends on what exactly you're talking about, but it's absolutely not true for improvements in cancer survival general. One alternative method is to look at per-capita death rates, for example:

Reduction in US and UK childhood cancer death since 2000 https://ourworldindata.org/grapher/cancer-death-rates-in-chi...

Reduction in several countries' age-standardized breast cancer death since 2000 (Why did it increase in South Africa? I'm not sure, maybe socioeconomic factors) https://ourworldindata.org/grapher/breast-cancer-death-rate-...

Reduction in global age-standardized cancer death rate since 2000 (Scroll down to second graph. Since the population is getting older, age-standardization makes a fairer comparison) https://ourworldindata.org/grapher/cancer-death-rates

2000 is an arbitrary year I picked for clear visual changes without needing to haggle over statistics. If you want to feel optimistic, switch the childhood cancer death graph to 1960-now.

This method has different possible failure points. It could be that less people are getting cancer, or that people who would get cancer are dying of other causes, or reporting of cause of death has changed, though this is very unlikely for some figures, such as leukemia death rates for children in the US. Statistics is hard. Overall though, the evidence is very good that cancer survival has improved a lot due to better treatments since 2000.

If you have a more specific claim you're dubious about, I'd be willing to look into it for you. I'm very enthusiastic about this topic.