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The way you worded your post, it read as if you had connected your bench supply directly to the battery.
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Of course I connected the charger directly to the battery. I chose to use a 5V charge voltage, but it could easily have been 6V or even 10V if used for short bursts - the critical voltage is the voltage that the battery pack has charged up to, not the charging voltage (which must always be larger than the critical voltage, or the battery would never get up to its critical voltage!)
We are not talking about a float charge here, which would be at the same level as the rated voltage, i.e. 3.7V.
The 2 essential criteria are charge current and the battery's state of charge - as you say, this must not exceed 4.2 volts, and must be checked regularly by disconnecting the charger and using a voltmeter directly on the terminals, a process that is automated in a smart charger.
One would normally charge at around 10% of the batteries current rating but it's possible to push Lithium batteries a bit harder, provided that you continuously monitor the battery temperature.