people like she/he are...

Seems pretty straight forward the writer made a mistake, it happens a lot with these helpful machines called computers which autocorrect, and if you type fast you could get one or two into your document. "Now recruiters like HER are increasingly looking..."
In your own Query the 'i' should be capitalized, "Query: Is the use of the word SHE correct?! there is also no need for the '!' nor is it accurate. The capitalization is a new phenomenon started since the internet became the medium of choice for communication, in the past it would be in quotation marks and NOT capitalized, as capitalization indicates SCREAMING AT SOMEONE in this forums, or emails. Perhaps underlining the word is an option if your concern is a possible confusion at reading time?

The word "like" is a preposition, and the pronoun is its object. Objects take the accusative case: 'him', 'her', etc.
The correct form of the pronoun is 'her.'

Will someone please inform Ron Paul that English speakers like he are incorrect in this case?

Yes, people like she is grammatically correct. Like in this case means "such as". People like her would mean people are fond of her.