He did hold on, and when she tried to pull away he tugged her back towards his chest, so the back of her shoulder hit it and he leaned in to speak near her ear. "I didn't spontaneously eject anything. I'd like to..." He smirked then, and lifted blue eyes back over to River, but still spoke quietly near Tex's ear. "It isn't my fault that thing's gone shitty." Telling him he was an AI. The idea was absurd. Church would hold Tex back with him as River pushed Delta back into his slot in York's head, willing to stand there and watch, but not willing to let Tex go forward to them.
He'd been the one who had just died. No one gave a shit about that. So he wasn't letting her go forward and give a shit about York, either. And while she may have want to do so.. Tex always liked it when Church showed signs of possession with her.