Does this sentence 'the researcher with all his assistants explain such claimed to be true' use correct grammar?

No, the sentence 'The researcher with all his assistants explain such claimed to be true' does NOT use correct grammar.

Correct examples:

• The researcher with his assistants explained their claims to be true.
  
• The researcher and his assistants explained such claims to be true.
  

Better:

• The researcher and his assistants defended their claims as true.
  
• OR, simply
• The researcher defended his claims.

Note: "All of his assistants" isn't really needed because it is assumed most researchers have assistants. The assistants typically do not take public credit, or defend the claims, unless they were on the team of chief researchers or the assistants present the results on behalf of the researcher.

"As true" is not unnecessary if you use the verb defended.