句子加 is 没有语法错误。其实，有没有 is 是believe 两种用法（句型）的体现。

He believes it true that purpose is what creates happiness.
He believes it is true that purpose is what creates happiness.
第一句结构：believe + 宾语 + adj.（宾补）
具体说，it 是形式宾语，true 是宾补，that purpose is what creates happiness是真正宾语。
第二句结构：believe + (that) 从句
具体说，it 是形式主语，is true 是系表，that purpose is what creates happiness是真正主语。引导宾语从句的that 被省略。加上就更清楚：
He believes that it is true that purpose is what creates happiness.
除了believe 之外，英语中还有这几个常用动词find, think, consider, feel，跟believe 有着同样的用法或句型。举例如下：
We thought it (was) necessary that the two sides should stop arguing. 我们认为，双方停止争论是必要的。
I consider it (is) best that you should stay here. 我认为你最好住这儿。
Under the circumstances I feel it (is) right that you should know this matter. 在这种情况下，我觉得你知道此事是对的。
I found it (was) strange that she had not come yet. 她竟然没来，我发现奇怪。
I think it (is) important that we should keep calm. 我认为我们保持冷静是很重要的。
 
除了使用that 从句外，还可以是动词不定式。例如：
We found it (was) quite pleasant to work with him. 我们发现跟他一块工作很愉快。
I felt it (was) hard to communicate with them. 我感觉难以跟他们交流。
He considers it (is) quite foolish to do like that. 他认为那样做很愚蠢。
I think it (is) difficult to do the job well. 我认为做好这件事不容易。
We believe it (is) useless to read without understanding. 我们认为，不理解的情况下阅读是没用的。