Ok, let me try to be clearer.
You can power a Teensy by
- 5v via USB. If you have not cut the solder jumper from VIN to VUSB you can draw about 500mA (3.0/3.1) or 350mA (LC) via the VIN pin if you are powering the Teensy via USB;
- 3.7-5.5v via the VIN pin. If you have cut the jumper from VIN to VUSB, you must provide power on VIN when programming the Teensy;
- Regulated 3.3v power to one of the two 3.3v pins.
No mater how you power the Teensy, the digital data pins will emit 3.3v when you do a
digitalWrite function call. Some pins cannot be used for
digitalWrite, and can only be used for
analogRead. I don't recall off hand how many micro amps you can pull off of a data pin on the 3.1. On the LC, it is 5mA for most pins, and 20mA for 4 pins.
On the 3.1 and LC, the DAC pin can emit voltage between 0 and 3.3v using
analogWrite (it may be possible to reduce the max. voltage of the DAC below 3.3v). You would not typically use the DAC pin for WS2812 or APA102 LEDs.
On the Teensy 3.0 you can draw about 155mA of total power from the 3.3v pin. On the Teensy 3.1 this is about 185mA, and on the LC it is about 120mA. While those are the limits in the datasheet, in the past Paul has recommended that you never draw more than 100mA for any of the Teensys. Hence when I'm doing WS2812's for costumes, I limit the total power to about 75mA, so that I can power it via the 3.3v pin.
For LED strings, if you are powering the LEDs via a 5v source, the problem is the LED microprocessor might not notice the transition from 0-3.3v as being high. Some will work with 3.3v, some will not. As I mentioned, I have a variety of neopixels from Adafruit, and the older ones have no problems with 3.3v data signals using 5v sources. The newer LEDS tend to be pickier and I have to do level shifting if I'm powering the neopixels via 5v USB power. If I power the Teensy via a 3.7v lipo battery, all neopixels will work correctly (and when I hook up the 5v USB to program the neopixel, some things will not work, and I need to unplug the Teensy from USB to see if things are working correctly). So, I would plan on having to do level shifting. As I mentioned for neopixel work (but not APA102), the LC is interesting because it has a free level shifter. But for APA102 work, you need to think of level shifting, and the 74HCT245 is the preferred level shifter.
As an alternative, I have at times thought about using a 5v processor (Polo A-star, Squarewear, or Adafruit Trinket/Trinket-Pro), but I usually keep coming back to the Teensy.