Thanks @Ted Yapo, I thought I was correct, for the reasons you kindly elaborated on. But sometimes you lose confidence when working in a new area! 

No problem.  I saw those comments when they were posted on the blog, but didn't bother responding because they're correct for most applications.  You just need to realize that you aren't dealing with one of them.

Besides, you can't win arguing against the Internet.

There are various rules-of-thumb for paralleling semiconductor devices, like it's OK for MOSFETs (mostly), but you need (emitter) resistors for BJTs and diodes.  LEDs, being diodes, fall into the latter category.  Generally, you should not parallel diodes (or LEDs) without resistors, because (1) there is some spread of forward voltage between LEDs and (2) the forward voltage drops with temperature.  The combination of these two factors can cause a situation known as thermal runaway, where one device starts to consume more of the power, leading to a higher temperature, hence drawing more power, etc. This is the situation described in the comments.  You won't have this, for several reasons.

First, with the power level you are driving all the LEDs, you can't even damage a single one (correct me if I'm wrong).  You will have to verify the numbers, but I think the peak and average power you are driving the LEDs with is within spec for just one of them.  So, even if a "complete" thermal runaway were to somehow happen, causing all the power to end up dissipated in just one of the LEDs, no damage would occur. Your LEDs wouldn't look balanced, but that's an aesthetic issue.

With the power you are talking about, you probably aren't going to heat the LEDs appreciably anyway.  If you are anywhere near the efficiency peak of the LEDs, you are seriously under-driving them.  5630 LEDs are "1/2W" devices (properly heat-sinked).  What average power are you driving them with? a few mW would be my guess.  This level of power might increase the die temperature by a few degrees, but that won't make any difference whatsoever.

The other thing to realize is that LED dice are actually paralleled without resistors in some commercial LEDs. The trick is good thermal coupling.  If the LEDs are close in forward voltage (e.g. matched or from the same wafer) and held at the same temperature by virtue of being mounted on the same substrate, they won't experience thermal runaway even at elevated current.  I have a bunch of multi-chip LEDs constructed this way.  If I were building multi-chip LEDs, I'd probably try very hard to put them in series, but manufacturers are using parallel arrangements and getting away with it.

The HaD blog comments you reference are well-intentioned but incorrect in your case.