What does "can be said to do / to be" something mean?

The various modern revolutions in physics, in psychology, in politics, even in literary style, have not escaped his intelligent notice, but they can scarcely be said to have influenced him deeply.

(Source)

Could you please explain the following?

They can scarcely be said to have influenced him deeply.

Or, I can not understand such a structure like the following:

In contrast, prices set by a central planner are necessarily arbitrary, since there is no standard against which they can be said to be correct or incorrect. d'oh!

Solution 1:

If something can be said to be X, it means that it would be possible (or better, accurate or reasonable) to say that something is X.

Look at the following lines, meaning (very roughly!) the same thing:

They can scarcely be said to have influenced him deeply.
It can scarcely be said about them that they have influenced them deeply.
It would be wrong to say that they influenced him deeply.
They did not influence him deeply.

For your last sentence, a similar exercise:

There is no standard against which they can be said to be correct or incorrect.
There is no standard we can use to say that they are correct or incorrect
There is no standard that defines them as correct or incorrect