For Play Integrity, you do have to have the Play Services installed, but that doesn’t mean you need to sign into Google :-)

(By the way, microG, an open source Google Play Services reimplementation, can achieve BASIC_INTEGRITY now, too. Which unfortunately doesn’t help much as most applications that do use Play Integrity want DEVICE_INTEGRITY at least.)

> but the companies choose lie of play store "integrity"

Agreed, very unfortunate. Most apps don’t even need it, but the security theatre is easier to do than actual security.