Jesus didn't speak specifically to that subject at hand in this passage, therefore there was no "word from the Lord", no quotes to offer up. Instead Paul did what he does in all his letters, which was address the situation and offer up a solution to the Church. In this particular case, they were concerned with marrying during a trying time where persecution of Christians was rampant, making life difficult. He simply offered up that they could go either way, but he preferred they remain single if they could, so that they were more easily able to withstand the tribulation to come.
At no point in this letter does Paul claim it was divinely inspired, so the quote in your meme doesn't negate that assertion. It's not that the statement isn't divinely inspired, but that the Lord didn't speak to it while alive on Earth.
This, of course, doesn't prevent anyone from just saying that none of it is inspired or from claiming that all of it is when the context is understood.
