Even if I didn't know what the 4th Amendment said, I would know that the above statement is wrong.
The Constitution specifically delegates to each branch of government certain limited and defined powers. Essentially it tells the government what it can or must do. If it ain't there, they cannot do it (constitutionally).
The Bill of Rights, on the other hand, doesn't authorize anything and doesn't grant anything. Those first 10 Amendments remind the Federal -- not national -- government that all other powers belong to the States or to the people respectively and enumerates SOME of those rights. As opposed to the Constitution telling the government what it CAN do, the BoR tells them what they SHALL NOT, MUST NOT, or CANNOT do.
1] They SHALL NOT make laws about speech and religion. They CANNOT prohibit you from worship. They CANNOT stop you from assembling.....
2] They SHALL NOT infringe on our right to KABA.
3] They SHALL NOT quarter soldiers.
4] They SHALL NOT search without a warrant. They CANNOT issue a warrant without probable cause and an sworn affidavit declaring what is to be searched and why.
5] They CANNOT compel you to testify against yourself. They CANNOT take your property, even for good reason without due process and fair compensation.
6] 7] 8] . . . .
You get the idea.
The idea that you could be searched without a warrant when it is 'reasonable' is just not true. Any search that fails to meet the 4th Amendment conditions is unreasonable and SHALL NOT be done. It is my right (and yours) not to be searched without probable cause that SHALL NOT be violated.
I understand that the courts and the 'law' says that government can do it, but does the law trump the Constitution? I think not and the Founders would agree.
That is an incorrect statement. UNREASONABLE searches and seizures are prohibited. That implies directly and logically that REASONABLE searches are permissible.
Warrants have never (that I know of) been a requirement for every search. Customs searches fit that situation.
Amendment IV
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
The idea that you could be searched without a warrant when it is 'reasonable' is just not true.
Obviously I have to disagree and I think that even current practice shows your statement to be incorrect.