I do. The only Google service I actually use anymore personally is GMail but that simply forwards to my iCloud account. It's easier and more efficient on battery to just check one mail account. I also ditched Google Calendar / Contacts for iCloud because they work almost exactly the same. Again easier to just use/sync one service IMO. I was never a big Google Docs user to start with but now I use DropBox and native apps. Again I only setup my DropBox once and it's good to go. I can use different (and more powerful) apps as needed. Sometimes Numbers on iOS is fine for quick data entry but for building out a big spreadsheet I'm going to most likely use MS Office on a desktop. I guess you could do this through Google Drive now but I already have DropBox setup so why bother? I use FaceBook/Twitter instead of Google+ which are both first class citizens on iOS/OSX now. FaceBook chat has replaced GTalk just because everyone I know uses it. A lot of this goes back to Google's period where they did a very bad job supporting iOS. The path of least resistance was just to use something else and now I have no need to switch back. From what I've heard their iOS apps have improved greatly but I'm happy with what I'm using.
Google Drive, OTOH, works on Windows/Mac OSX/Android/iOS (and probably WP7, Windows 8, Blackberry, etc, but I haven't done my homework). Dropbox is another option.
Personally, I would never use iCloud. It's not because of trust, it's because of portability. What if I have an iPhone, then decide to buy a Samsung phone? I can't use iCloud on that device (AFAIK), so I'd have to transfer everything manually. What if I change from Android to Windows 8? AFAIK, Google Drive will still work.
If you're so bent on trust, then use Dropbox. It's much more portable and they don't really care about your data, just your monthly investment.
He's willing to use the iOS ecosystem and it satisfies his requirements and it's convenient for him.