Key feature brought by HCE is that, when NFC device is in Card Emulation Mode (CEM), all data coming from NFC controller are routed towards device's CPU (read Android OS) by default. This was not the case before - when default routing in CEM had been towards secure element (SE). Storing sensitive data in OS memory raises severe security issues - the ones you asked - in the case when device is "rooted". There are two ways to mitigate those security risks:
A) Provide more secure location for sensitive data
This "more secure location" could be Trusted Execution Environment (TEE) - Special part of CPU that runs its own separate OS and therefore is not compromised when the main OS is rooted. On the security scale, TEE provides more security then OS and "SE in the cloud", but less than SE. If TEE is not enough (which is the case for services such as open loop payments, authentication services - ID cards, passports) nobody forbids you to use SE on the phone that provides HCE service. In that case, default routing to CPU (Android OS HCE service) can be prevented by using routing tables (data intended for application with specific AID is routed towards SE).
B) Implement security mechanism to make existing location more secure
If you don't have TEE and can't use SE, you can make things more secure by using techniques such as: user verification (something "that user knows" like PIN, or even better if possible "something that user is" - biometrics), transaction constraints (low value transactions, limited number of transactions in one time-frame, etc), tokenization, doing Android OS checks prior transaction (i.e. does user have root priviledges), etc.
The best is to combine A and B.
What you need to understand is that HCE is not intended for high security services. Look on HCE as more-simple-but-less-secure solution, intended to accelerate adoption of NFC services. It has great added value for SPs that can accept a reduced level of security in exchange for an improvement of other factors such as time to market, development costs and the need to cooperate with other parties.
You can read more about this in document written by Thom Janssen & Mark Zandstra, people from UL-TS (former Collis), named "HCE security implications". You can download it from here: http://www.ul-ts.com/downloads/whitepapers/finish/6-whitepapers/289-hce-security-implications.