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BufferedReader.readinto() should also raise BlockingIOError according to the docs. Updated unittest checks for that also.
BTW, The documentation for BufferedIOBase.read() says that BlockingIOError should be raised if nothing can be read in non-blocking mode. BufferedReader inherits from BufferedIOBase and overrides the read() method. This is the documentation for BufferedReader.read():
 read([n])
 Read and return n bytes, or if n is not given or negative, 
 until EOF or if the read call would block in non-blocking mode.
This sentence is complete gobbledygook, and it makes no mention of what should happen if nothing can be read in non-blocking mode. So I presume behaviour for BufferedReader.read() should match the documented behaviour for BufferedIOBase.read().