I agree with the over all message here... the host is maybe a little overly dramatic.
But I think we need to be careful of building a doctrine on one verse, especially when we consider the audience of who Paul was talking to here.
But Rom 3:11; is only part of it. There are many more verses that say the opposite.
Matt 6:33; "But seek first His kingdom and His righteousness, and all these things will be added to you.
Matt 7:7; "Ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you.
John 7:34; "You will seek Me, and will not find Me; and where I am, you cannot come."
John 8:21; Then He said again to them, "I go away, and you will seek Me, and will die in your sin; where I am going, you cannot come."
Now these two verses could be a problem, because they Him... but they don't find Him... still the fact remains... some seek Him whether they find Him or not.
Acts 15:17; SO THAT THE REST OF MANKIND MAY SEEK THE LORD, AND ALL THE GENTILES WHO ARE CALLED BY MY NAME,'
Acts 17:27; that they would seek God, if perhaps they might grope for Him and find Him, though He is not far from each one of us;
Heb 11:6; And without faith it is impossible to please Him, for he who comes to God must believe that He is and that He is a rewarder of those who seek Him.
Isa 55:6; Seek the LORD while He may be found; Call upon Him while He is near.