Step one, don't assume.
Step two, understand 3-ways a bit better. They don't have an "on" position - one traveler is hot when the switch is one way, the other traveler is hot when the switch is the other way. Both ways are "on" in the sense that power is connected from the common to a traveler - whether that turns the light on or off depends on the other switch (or switches, if a 4-way is involved.)
Are there more than two switches that control this light, or do you have mystery switches that you don't know what they do?
Normally the switch where power comes into a 3-way (on the common terminal) has no direct connection to the light - it only connects to the far-end-switch on its travelers, and the far-end-switch connects (on its common terminal) to the light. If you have a black and red traveler leaving one switch, and red and white travelers at the other (where the black probably DOES connect to the light - that's why there's no power on it) there's either a 3rd switch (would be a 4-way) or a junction box in-between.
If there are only two swichesswitches, the likely junction box is the light, where the neutral in this 14-3 cable will meet the light, and the travelers (black and red from the power supply switch) will connect to white and red to the far-end-switch, and the black from the far end switch will connect to the light. The white wire should be marked with paint or tape in a hot color at both ends to indicate its use as "not a neutral."
None of this is "non-standard" - if the switched hot was white, that would be non-standard and a code violation, even if it was marked. Unfortunately not uncommon when sloppy work was done, but not correct. The described wiring appears to be correct so far. If you think "white is always neutral", you have a bit to learn, even in the present day when it usually (but still not always) is.
