No, for security reasons it is not possible to access android log files on the Nexus 7 without root access. Google changed that with Jelly Bean.
I'd suggest you wait until logcat readers like aLogCat and such get fixed (i.e. they will require root access to show all logs then).
It has been found that the READ_LOGS permission allows access to many protected things (source) such as:
All solutions below require root access:
You need to either run logcat as root in a shell or manually grant it via the shell pm command (root required) works also (see XDA, exchange org.jtb.alogcat.donate with the app's pkg name):
pm grant org.jtb.alogcat.donate android.permission.READ_LOGS
This is for the lazy ones and not suggested:
If you're desperate, careless and lazy, you can fix it by giving every app the READ_LOGS permission by applying this ugly and insecure hack (Chainfire via twitter):
chmod 04755 /system/bin/logcat
To quote CyanogenMod developer Koushik Dutta's G+ post:
Did the Android Log permissions/behavior change in JellyBean?
It seems that if an application runs "logcat" now, it can see only the log entries created by its UID. Log lines from other UIDs are not shown. Basically, it seems to be filtered now.
I have the same permissions as usual. Also confirmed the same thing is happening in other log collector apps.