The statement is actually correct.
an average protein molecule present in the human body has around 300 chemical units called amino acids
This refers to an established scientific fact.
If we reduce the statement:
The researchers, including those from the Salk Institute in the U.S., said that the microproteins had fewer than 100 of the building blocks.
"Had" (past tense), here, is referring to the research they did/observation they made (in the past).
If the researchers wanted to claim it as a fact, the statement would use "have" (as "microproteins" is plural):
The researchers, including those from the Salk Institute in the U.S., said that the microproteins have fewer than 100 of the building blocks.