I was told by a Reformed pastor that nobody can ever have assurance of their salvation. Is this an accurate Reformed perspective?

​According to him, we can't know if we'll persevere or not, and we should never have total assurance. He gives an example like this: "You ask me: 'Do you know you are saved?' My answer: 'Yes.' You ask me: 'Do you have assurance?' My answer: 'Yes.' You ask me: 'Why do you believe you are saved?' My answer: 'Because today I am still believing.'" He also says to constantly examine ourselves every day to see whether or not we're persevering—because we could all have false faith—and he praises the Catholic Church for warning against "any necessity of infallible assurance." So basically, according to him, our assurance of salvation should hinge on whether or not we are still believing.

​Now, I'm not Reformed, but I am curious about the theology, and I wanted to see if this is actually a standard viewpoint. I did notice that he mentions nothing about Christ when it comes to assurance of salvation, which caused me to raise an eyebrow.