这属于“否定范围”问题。表面否定谓语动词，实则否定 too，不包括 careful。是网友自己理解失误。

too：过分

not too：不过分

You can’t be too careful in doing the experiments.

你在做实验时，仔细的程度不会过分。

请看北大董桂枝教授《英语特殊表现法例解》上的说明：

cannot...too...（无论怎样......也不过分）。例如：

You cannot praise the play too highly. （这出戏你无论怎样称赞，都不会过分。）

One can never be too careful in one's work. （工作越仔细越好。）

cannot...too...的意思是“it is impossible to over+原形动词”，译为汉语是“无论怎样......也不过分”或“越......越好”。句型中too是“过分”的意思，它可用表示“过度”意思的词如“over+原形动词”表示，cannnot可用impossible和difficult表示；如果不用cannot，可用can后跟hardly, scarcely，例如：

It is impossible to over-estimate the importance of the development of industry in China.

=We cannot over-estimate the importance of the development of industry in China.

=We cannot estimate too much the importance of the development of industry in China. （在中国发展工业，无论如何重视也不为过分。）

We cannot pseak in terms of too high praise of his merits.

=It is impossible/difficult to speak in terms of too high praise of his merits.（他的功绩无论怎样赞扬也不为过。）

You cannot pay too much attention to your pronunciation.（你越注意你的发音越好）

I cannot thank you too much.（无论怎么感谢你也不为过。）

       can't (或cannot)...too... 和 can never ...  too 都是惯用语，意思都是“无论怎样...也不为过”、“越 ... 越”。如：

       One cannot be too faithful to one's duties. 一个人对他的职责多忠实都不为过。（=一个人对他的职责越忠心越好。=对职务再怎么忠实都是不过分的。）

       We cannot be too faithful to our duties. 我们无论怎么忠于也不为过。

       You cannot be too careful in the choice of your friends. 你在择友方面再怎么小心也不为过。

       We cannot admire her beauty too much. 我们怎么赞美她的美丽都不为过。