I think that my I2C bus is crumbling down at 670kHz. The sketch for the webpage is the resulting sketch with the client.prints. I tested it with your sketch with and without Serial.prints, with and without delay and so on. I even did Serial.flush() everywhere to be sure that the Serial library was not longer busy. The result was still the same.
I was assuming that my I2C could be best at 100kHz, because of wires and Arduino Slaves, but now I feel confident to use 200kHz 
Well, I didn't buy an oscilloscope (yet) : budget USB oscilloscope - General Electronics - Arduino Forum