The alternate interpretation has him, the thinker, thinking back at the time when he, the thinker, first picked up a Wall Street Journal at his first job, the thinker's first job, in the early 1920's.
This leaves Mr. Jensen hanging about as pretty much irrelevant to anything else in the sentence. At this point we need to ask ourselves if anyone would seriously consider writing such a bizarre sentence. The answer is no, and we must revise our hypothesis about the possible meaning of the sentence and roundly reject the alternate interpretation, no matter how technically correct it is.
This is, however, a wonderful analysis in terms of work with machine translation or machine understanding of language. It is the sort of analysis that is necessary in order to program the machine to reject the alternate interpretation as "off-the-wall", because with less sophisticated programs the machine is going to "think" that both interpretations are equally good.
CJ