They are presumably referring to the National Intelligence Law of 2017 that China passed. That law requires companies to assist the Chinese security services with surveillance and espionage. It's similar to laws in other countries such as the United States (National Security Letters via the Stored Communications Act) and United Kingdom (Regulation of Investigatory Powers Act).
So there is some legal basis for the Chinese government to be able to "access" Chinese products, in the sense that the manufacturer may be required to assist them in doing so by revealing encryption keys or installing backdoors, but there is little evidence that the law has ever been used. Also due to the design of many products it would be difficult, if not impossible to grant such access without it being quickly discovered and damaging the company's reputation.
For example, much has been made of Huawei's potential cooperation with the government, yet no evidence of access via this law has been presented. For what it's worth, Huawei claims that it would close down the company if legally required to provide access to Huawei products.
As such, the claim is technically correct in the terms it was stated. However, to answer your question, can the Chinese monitor and copy all information passing through he device, the answer is no. Even if it were technically possible, such massive and systematic exfiltration of data would be quickly discovered.