The radionuclides expelled from Chernobyl are known and traceable, not being found in nature they can be detected easily. Knowing their decay chain over time and, later, the bioaccumulation of those isotopes (based on how people will come in to contact with them) you can start to figure out how tissues that bioaccumulate or come into contact with an alpha source could react.
What I am saying is, it's important to understand that its not just about 'radiation' may equal 'cancers'. We know how to understand this deeper than that, on how to measure and calculate health effects based on the specific isotopes and their related exposures on tissues, primarily internally — because alpha decay has the highest energy but is easily absorbed by paper or the outer epidermis, to do damage it has to be in close proximity to sensitive tissues. So its important to stick to those more calculable and verifiable hypothesis rather than broad 'radiation' and 'cancer' labels.