Led's are current operated devices. The voltage drop across them is nothing more than a practical nuisance. The ideal led would behave the same as an ideal zener diode. Below a certain voltage, they would draw no current. Above a certain voltage, they will draw as much current as the supply can deliver.

In your case, it only works because the leds are not perfect zeners, and the battery voltage just happens to be at one particular sweet spot. What happens when that battery is being charged, and the voltage is approaching 15 volts. What is your led current then?

And if resistors are bad and waste heat (energy), what do you think that red led is doing, especially if you cover it with black tape.

The correct way to power an led is with a constant current source, so that the current remains constant irrespective of battery voltage. A series resistor can approximate a constant current source over a limited range of input voltage, if the difference between battery voltage and combined led voltage is high enough.

Some worked examples;
R = E/I
E = Vbatt - Vled
I = 20mA
Vled = 3.6 volts
Vbatt = 11 to 15 volts

for one led, the resistor value at Vbatt = 11 volts is
(11 - 3.6) / 20mA = 370 ohms
when Vbatt is 15 volts, this resistor will give an led current of
(15 - 3.6) / 370 = 30.8mA

for two leds, the resistor value at Vbatt = 11 volts is
(11 - 7.2) / 20mA = 190 ohms
when Vbatt is 15 volts, this resistor will give an led current of
(15 - 7.2) / 190 = 41.1mA

You can see the trend. I leave it to the interested reader to calculate values using 3 leds.

With LEDs resistors are the GREATEST invention to protect the LEDs for over current and burning up.

The LED voltage varies from maker to maker and, as well, also this due to temperature variables that the LEDs suffer.

LEDs are NOT voltage devices, LEDs ARE CURRENT devices, in principle.

Best, BEST is a PWM constant current source which reduces the Resistors LOSSES if well designed.

Do not try to CIRCUMVENT Physical and electric principles.

"Do Not use Internet LED math"  It is always wrong.  Always.  
Measure the ma.  You did that, and that is good.

The circuit in the photo is like a garden hose.
If it's going in one end, it is coming out the other.

Guessing the red LED is high Eff.  Meaning mostly it is like on the front of a VCR and lights up well with 1ma, but is not bright with 20ma.
Great for the VCR or DVD, but it won't light up a room.  The red frequency will help if the room has any stuff in the red spectrum, so don't cover it.

The 17ma is luck. (because the math is wrong)

A 12V battery is 'dead' at 11.9V.  This battery was at 11.8V.
A full battery at 12.67V, or a charging battery at 14.4V will have MUCH different readings.

If the battery was at 13.0V, I would expect the current to around double, maybe more, with the thoughts I have right now.  Shortening the life exponentially.
LEDs are fickle creatures regarding V:I.  You never can tell.
My last batch of LEDs run over 60ma at 3.6V.

I prefer the resistor as a current limiter. For a few reasons...
-It gives an indication of the battery voltage.
-The ma are reduced (longer battery life) as the battery voltage is reduced.
-No stuff to fail. (when is the last time you saw a resistor fail if nothing else caused it?)
-It won't go "Click!  I'm done. It's dark now." or flicker at the end.
-There is plenty of warning before the battery is dead and leaves the area dark. Sometimes months, because they are running at <2ma.
-The losses are very small in a well designed light, with good LEDs.

First, Basically, when LED's fail, they often fail to a short circuit.  In your case, with 4 led's in series, if one fails, they will likely all fry in the string as has been my experience with similar setups.

Second, the light output varies dramatically with the battery voltage.  It the battery is full, the light will be bright, but when the battery is discharging, the light output will reduce dramatically.  

Third, not all LED's in even the same batch have identical Vf and Imax, or possibly these values change over the life of the device.  From my experience you get better results in the long run if you don't drive them near their limit.  The LED's efficiency appears to be a bit higher when not driven so hard.