This is entirely false: Password managers and their hosting do not have access to your passwords. Comment author may have misunderstood how respectable password managers work, and I'd suggest they Google for more details.

The master password you use to unlock the manager is used to encrypt the passwords themselves along with other metadata.

It is the strength of the master password that guards the passwords within.

Indeed, you are trusting their software to be correct and safe like you would any other software and vendor.