honestly, this is not true at all. PSP offered tons of different experiences, and the fact that most people ignored their existence in favor of the big console-like games proves that it's exaclty the opposite. luckily, I haven't heard this myth in a long while
Most of those experiences failed to find a large audience globally, which is the point. If you look at the games that were unique to the DS - your Laytons, your Nintendogs, your Devil Survivors, your TWEWYs - they were the games driving system sales. And that's in spite of there being rampant piracy on both DS and PSP.
The more "handheld-like" experiences on the PSP weren't driving hardware sales or software sales in the west. Games like Project Diva weren't even released overseas (and if they did, they'd see a similar sales fate as the PS3/Vita/3DS games), stuff like Z.H.P. and LocoRoco failed to resonate, as did Practical Intelligence Quotient (Sony's answer to Brain Training in marketing). Games like Tactics Ogre: LUCT, The Third Birthday, Ridge Racers 2, while great, again, didn't resonate with the market in the same way.
There's a reason DS didn't succeed off the basis of console-like experiences like Mario 64 DS and Metroid Prime Hunters, and instead the games driving its massive install base were entirely new IPs and new games, not riffs on existing ones.
This didn't happen with PSP outside of Japan, the big sellers were PS2 derivatives, which didn't have the same reach. Then, ironically, Sony shifted to the kids' market with PSP in its later years, despite the stigma Nintendo once got for being "kiddy". The DS ended up getting the DSi XL - aimed at an older audience.
This chart says it all really. PSP software sales were minuscule compared with other platforms at the time, and in a region where Sony platforms are well received.
I'm not saying PSP games are bad, or worse, or anything like that, just that the games that the format played host to didn't resonate with the masses. Personally I never really liked console-style games on PSP, I favoured arcade games (Ridge Racers 2! OutRun 2006! Project Diva 2!) and games made for the smaller screen (Tactics Ogre: LUCT!, Yggdra Union! Star Ocean remakes! Star Soldier remake!).
But it's clear that DS and PSP both played host to very different experiences too. For enthusiasts like ourselves, that meant that both platforms were essential. But you can't really claim that the sort of games that were popular on PSP weren't what led Sony to miss out on a roaring success.
There weren't any games that performed like this globally on PSP, for instance:
DS had dozens of success stories like that, and they all happened to be games that PSP just didn't have, or couldn't have due to its traditional control inputs.