You can correctly say that you approached something nearly, but it's not correct to say that you nearly approached something. Using the adverb 'nearly' as if it were the adjective 'almost' is generally not scholastically regarded as incorrect when the word modifies a noun, however, when it is used to modify a verb, it is logically incorrect, albeit not uncommon.Like I said, a lot of people don't understand the rule about placing modifiers close to what they modify.
Probably wouldn't make much of a difference.
"I nearly made $50 today" vs. "I nearly made $50 today."
Compare those two with the following:
"I made nearly $50 today."
The choice in the first two examples is between making some money and making no money at all because the adverb is modifying the verb, not the money amount that was earned.
I agree with your main point in the quoted post; however, I think it is noteworthy that emphasis emplacement can give the sentence "I made nearly $50 today." 5 different meanings:
I made nearly $50 today; you made nothing
I made nearly $50 today; I was given only $25.
I made nearly $50 today; yesterday I made over $50.
I made nearly $50 today; yesterday I made only $25.
I made nearly $50 today; yesterday was better.
The difference can be viewed as of the 'as distinguished from' type; the emphasis creates an appositionary effect in an imaginary contrasting sentence.