Pretty sure DLC can't have the Limited Profile tag, actually.

Rather, the issue for DLCs is that the Steam API flat out doesn't send out ownership data for DLCs. (As such, we'll never really know whether they take LPF settings from their base game or not. :P)
Due to that, any DLC, as well as any package with at least one DLC, will never properly show ownership on SG, regardless of whether the game is Limited Profile or not. I

There's actually [historically] several other reasons why the API won't send out ownership data, as well. For example, a game won't send ownership data properly for the first 24 hours after its release. Similarly, it won't send ownership data while it's in pre-order / pre-release. So, say that you've gotten an early key for a game via kickstarter backing it, and then someone posts a pre-order giveaway for it; You'll still see that individual being able to enter for the game.

Of course, for both of those circumstances, it may be that the existence of Profile Features Limited has made it so that neither is encounterable any longer (unless there's, say, a circumstance where AAA have some sort of immediate exception to the Profile Features Limited tag, or where a game has a limited beta access purchase period). Due to that, it's likely that PFL has effectively absorbed those elements, making it so that the reason for an API recognition error is almost exclusively going to be due to a DLC being involved or that the game is PFL.

I say almost exclusively because, those two common issues aside, it should also still be possible to encounter the issue where a listing is misconfigured (for example, an all-base-game package that doesn't properly send out data that it has any games in it, meaning that [despite having no DLCs] the package still can't properly be checked for ownership). Game Expansion listings (something of which Steam had a small number of during its earlier days, but hasn't seen any recent additions on) have also historically had recognition issues. While I'm not sure if this particular one is affected, this is the kind of listing I'm referring to.

I may be forgettting a few possible factors, as well.
The DLC thing and PFL are really the only two that an individual really needs to keep in mind, though, since they're rather prevalent.

P.S.
Between DLCs being rare in bundles and most users not wanting to deal with the hassle of manually adding people to Steam to check whether they already own the DLC or not, they're rather rare things to encounter on SG. :X
Ergo, people who post (non-soundtrack) DLC giveaways are inherently awesome. ^.^

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