If possession ,in this case, has occurred, and I have many reasons to believe it has not. Then it was invited....for when you play with that which the enemy entices you with long enough you will indeed get sucked in.
There are many cults and false religions who entice people and profess supernatural events......many which have been proven to be otherwise than from God for Satan does present himself as an angel of light.
So again, in this case , if it’s as they say, and much is not IMO ,...then it was by invitation and not simply leaving an opening.
Yes in that sense, both God and satan come in by invitation only.