My bad, you are both right - must have had too many Red Bulls and Vodka when I posted that...so the short answer is no, you will always have both, for now anyway.
That may very likely change down the road as polices are being added to the measly few that are in BES10 now.
I understand why you need that functionality...so here's what you can do...
Remove yourself off the BES (done from the device) and just go straight to EAS on your Z10. It's going to have all of your business accounts there - and if you want to add personal accounts, you may without the stupid tabs. I did that. I hated having to hit those stupid tabs every few minutes and hated not having access to my SD card through work, amongst many other idiotic things. You will lose absolutely nothing and gain so very much this way. There are many technical issues and bugs with BES10 that you may have already seen, so removing your BES account from the device and going EAS mitigates much of that horseshit. And it really IS horseshit.
Because you're on BES10, you are already EAS enabled. Here's the good news, you don't have to actually remove the user account on the BES, you can be just on EAS and the user account will still be on BES, just no device associated with it when you remove the BES acct on your device.
Then you setup the EAS account on your Z10 (choose Advanced/Exchange).
You will need to know your Domain username and password and the internal domain name (ie; domain_name without the extension, like "microsoft" without the .com), as well as the server name (like "server_name.domain_name.com" or .ca or whatever your external domain name is). Leave everything else at default. That should work unless they use non-standard ports, which most don't.
I'm the BES admin at our enterprise and while I have several users on BES-X/ BES5 and BES10, BES10 just annoyed me more than anything and offers nothing more than straight EAS. So I removed my Z10 from our BES and I couldn't be happier!
BES10 is not all that great for users IMO, but only for the IT admins, as they can set policy for all users with a single action. It's also more secure for the enterprise, but in a way that is so cumbersome for the user, it's more of an inconvenience than anything else, so trust me when I tell you I feel your pain.
I'm anti-BES10 personally...and we have a 35-user BES10 license. BES10 is nothing but a nightmare for most users...
For those who want to flame me about this post, until have have used Balance on BES10, don't bother posting here about it...because you have no clue and I will just tell you to F-off.
PM me if you need help with this -