Rashly as he behaved,he didn't deserve the punishment.

参考译文：虽然他举止粗鲁，但是不应该受到这种惩罚。

as引导的倒装让步状语从句（状语提前句首倒装结构）

书上译文是：……，但并未受到应得的惩罚。（=惩罚轻了）

我觉得应是：……，但不应受到那么重的惩罚。（=惩罚重了）

解答如下：

你的理解是正确的

（sb deserve sth=sb should have sth/receive sth)

deserve   vt.应得;应受;值得

(英文解释：If you say that a person or thing deserves something, you mean that they should have it or receive it because of their actions or qualities.）

Government officials clearly deserve some of the blame as well.  

政府官员显然也应当承担部分责任。

They know the sport inside out, and we treat them with the respect they deserve.

他们对这项体育运动了如指掌，我们也给予了他们应有的尊重。

He deserves a reward for his efforts.
他积极努力,值得奖赏。

You've been working all morning—you deserve a rest.
你已做了一个上午——该休息一下了。

The question deserves consideration.
这个问题值得考虑。

综合上述，你的理解是正确的