Interesting question! Not sure. IIRC, the max current that's spec'd for an Arduino pin is 20ma, so the 16ma of Rx is pretty close to that. If using the RFM69HW module, you could easily go over 20ma on Tx if you aren't careful.
An I/O driver can be modelled as Vcc with a series resistor when driving high (i.e. the resistance of the top FET in the I/O port), and a resistor down to ground when driving low (i.e. the resistance of the bottom FET). I/O currents are specified at logic levels. So for example the max 20mA I/O spec will mean the driver will drive above the logic 1 threshold plus a noise margin at 20mA. Often this is 2.4V with 3.3V Vcc, that means the output impedance of the top FET when drivng high is a maximum of (3.3 - 2.4)/0.02, or 55R. Similarly driving low will drive below say 0.6V when sinking 20mA, so that's a resistance of 30R. Note that the maximum current at logic levels isn't usually specified, although short circuit current is. Note it is also usual to have a stronger driver in the low state than the high state, specifically because a logic level 0 is closer to ground than a logic 1 is to Vcc.
In other words, you won't get 20mA drive current with zero voltage drop from the driver, so you can't generally use a pin for supplying that kind of current. What you should do instead is use a buffer like a FET to reduce the output impedance so that it can supply the current without much voltage drop.
Mark.
Edit: This is also the reason why it is better to drive LEDs that require more than a few mA with active low rather than active high signals. Since the output impedance is lower when driving low it allows you to control the current better with an external resistor.