I've had some experience using TTL level devices with a Palm device and with PICs. I suspect the issues with a Handspring are similar,due to the incestuous nature of the two design teams. The Handspring folks were formerly Palm people.
In practice, most modern RS232 switches at around a volt, not zero volts, so that +-12v RS232, +-5v. RS232, and TTL devices can be interfaced.
Any well designed serial device should have protection from +-12v. on its RX line , though maybe not on its TX line, leaving that to the receiving device. Put in a 22K resistor to limit current and a diode to block the negative voltages on the Picaxe RX line and you will protect against even +-12v signals, just like the Picaxe Programming interface does. If you are really paranoid, put in a 220 ohm resistor on the TX line as well.