Alternatively, make the log file available on a password protected web server. This web server should really be the same one that is watching the webhooks, but it doesn't have to be. If it isn't then just make a configuration setting that gives the URL base.
This is an interesting one because it requires coordination between the build script and build-buddy. Somehow need to return values from the script to build-buddy. Data could include:
Code coverage numbers, but unit test, UI test and combined
Lines of code, by language perhaps Obj-C, Swift, etc..
Time that the different builds took
Number of builds over a given time frame (week, month, year) including number of failures and successes and different types.