Well, not exactly free. I have noticed that you don't need to purchase a Quickening to obtain them, however. On my current playthrough I have been using only 3 characters (as usual for me). I did a bit of power-leveling at the beginning of the game (level 35 before sneaking into the palace), so I had no need to purchase the Quickenings for anyone but the characters I use--to obtain their 3x MP bonus. Anyway, I get up to the gate before Giruvegan where you need to summon Belias and, not wanting to give him to my main party, I give him to Vaan. Now I had almost forgotten to purchase him one and backed out to the main menu. As I was choosing him again so I could buy one, I happened to look over and notice that he already has one.

I don't know how many people know about this since I couldn't find anything about it in the official guide I have nor the online guide I use, but it sure came as a surprise to me.

I'm not sure I understand everything the way you worded it, as it's kind of confusing.
Are you saying you got there before having licensed Belias to anyone, gave it to Vaan, and Vaan never activated any Quickenings, but after doing it you saw that he got a Quickening (Red Spiral) before activating any on the board?

It's really not clear, I had to read your paragraph about four times to understand it and still not sure I do.

Heh, I have a way of talking in circles I guess. Here are the steps simplified:

1) Got to Giruvegan's gate without buying any Quickenings for Vaan (just to explain background info...this can be done at any time you can purchase an Esper)
2) Bought Belias for Vaan (can be done with any Esper/character)
3) Got Mist Charge without having to buy Quickenings (Was awarded the gold circles next to the name and the multiplier on max MP)

Right now Vaan has no Quickenings bought, but has the gold MP bars and 3x normal MP that you would normally get for buying them. I can summon the Espers, but still can't use a Quickening (Red Spiral, etc.) because none have been bought. I have just tested this with all of my characters that hadn't purchased a Quickening. The moment they bought the Esper, they instantly received the Mist Charges required to summon it. Thus you can actually get 3x MP without needing to buy the Quickenings. Even with this, you still have to buy the Quickenings in order to use them. This trick only gives you the gold MP bars and extra MP. I guess the advantage of this would be that you can get the extra MP for fewer LP. Buying all three Quickenings would cost a total of 150 LP, whilst buying an Esper could be cheaper (for 90 LP you can buy Famfrit and get the same bonus).

Another interesting note I found out while playing around this afternoon is that the extra Mist Charges count when preforming the actual Quickenings:

1) I bought an Esper that required 3 Mist Charges to summon (Famfrit for example)
2) That character got the 3 Mist Charges (As per what happened above)
3) I bought 1 Quickening (Let's say Red Spiral for Vaan)
4) I used the Quickening on an enemy and was able to use it 3 times before needing to use the "Mist Charge" option

Using this I was able to get a 19 hit Quickening chain with just Vaan. I don't really see any advantage to this because getting a lot of weak hits really doesn't do much damage.