When at my desk, I plug in through a Mont Blanc FiiO for my Beyerdynamic headphones. Makes a big difference with some audio. Wireless buds are obviously already a step down from wired, and one step further from amplified cans. And yeah, I'm an outlier and want to be.
So yes, the previous poster could conceivably be doing the thing that they said they were doing.
[1 PDF] https://www.innerfidelity.com/images/SennheiserHD600.pdf
What became of it?
But at lowish volumes (used most of the time, don't destroy your ears!) then yes, phones tend to have reasonable headphone amps in them. With decent power output and lowish output impedance. Unlike most computer motherboards, which have excessive output impedance and out power is so low I'd call anemic, when not flawed in other ways (noise due to poor isolation, or non-flat frequency reproduction due to shit implementations of aliasing filters).
I mostly connect the headphones to the phone to play rhythm games like Love Live sif, allstars or idolm@ster deresute, mirishita. My phone (chinese and a few years old) does very successfully drive the HD600 to a pleasant output while playing these games.
As an aside, I absolutely recommend Sennheiser HD600 to anyone who wants a durable (plus tool-free modular with good availability of parts, and compatibility with HD580/58x/650(aka 6xx),660S parts, thus effectively forever) all-rounder open back headphone with a focus on accuracy that's cost efficient and extremely comfortable. Plus they've been around for a good two decades, thus there's no shortage of reviews to base a purchase decision on.
[0]: https://www.audiosciencereview.com/forum/index.php?threads/r...
[1]: https://www.audiosciencereview.com/forum/index.php?threads/m...
Most headphones do sound colored relative to the HD600, but the key word is 'offensively'.