Okay. So. We all know the famous scene: Sayu walks into the room when Matsuda is visiting, and he's pretty much floored. What with "I think Matsuda-san is a good-looking guy! ...If you were younger, I'd consider dating you" - it's pretty damn obvious she's deliberately teasing him.
Of course, that's just in her mischievous nature, which is a moot point for at least a good while after the kidnapping. But let's take a look at what happens while Sayu is in danger, from Matsuda's end.
Of course, Matsuda is an incredibly emotional person, and anyone would be very upset to hear that a family they've grown close to is being torn apart. At this point, these pages don't mean any more than that.
They do when you look further ahead, though.
During the kidnapping, Matsuda was in L.A. with everyone else, working - or trying to work - on getting her back safely. The only time he's shown during the whole fiasco is here:
IGNORED. At least outwardly. Light, you could have at least afforded an "okay, gotcha." Asshole.
Anyway, frustrating, huh? Sayu got home safely. Matsuda wasn't asked to do anything to help that happen. Frustrating as hell. So, when her safety is threatened again...
Impulsive as usual, of course. But damned if he could let Sayu be in danger again. (Also note that Soichiro doesn't say Matsuda is useless. Aww.)
Impulsive is right. And he gets a hard time for it.
Okay. Fast-forward.
We know Matsuda is always giving Ide a hard time about being clueless when it comes to love.
WHY? No, really - some of the comments seem so out of the blue. This one at least is prompted more obviously:
This next one, however, is bizarre at first glance... and probably second and third and fourth glance, too. It appears to be an absolute non-sequitur, and could even point to Matsuda/Ide... if you've got your slash goggles on and aren't looking at what leads up to it and don't realize that it's not at all random.
... Catch it?
Throughout the second arc, Matsuda is accused of being weak or impulsive - Aizawa glares at him whenever info appears to have leaked. When Matsuda tries to ask a serious question, Aizawa, in effect, says "Since when do you take anything seriously?" His confidence is fragile, and as is shown above, he's quick to get defensive about his impulsiveness.
Light says that between Matsuda and Mogi, it's better that Mogi is the target - Ide clarifies that this is because Mogi wouldn't say anything stupid. Insecure about it as he is, this comes off to Matsuda as a jab at his impulsiveness, especially when preceded by a mention of the time he risked his life to keep Sayu out of danger.
The comment was not random. It was a defense for why he acted on that impulse.
He... he had it bad. From that one little interaction at the Yagami household, he fell hard for her. Which doesn't seem like it would be a difficult thing for Matsuda to do, granted. He's quick to make judgments, very heavily influenced by first impressions... it explains why he pretty much never suspects that Light is Kira, regardless of whatever evidence may pop up. He's a rationalizer.
But I digress. Point being: perhaps for any other character, it would be ridiculous to say they fell hard enough to risk their life for the other person after one short interaction - that is, unless you're talking about Misa (and in this respect, Matsuda is rather similar to her). But when you think about it, it wasn't just that short interaction - it was supported by the fact that she's a Yagami, and that he loves that family. And you could say that Matsuda defended her life out of familial love. But, given the flirtatious nature of their encounter at tea, leading up to the comment to Ide... I am pretty sure that is not the case.
...But there are two sides to a ship, right? Sayu has to like him back, right?
This is where it gets horrifically speculative on my part, and you might say I just want to see Matsuda and Sayu live happily ever after. And indeed, that's part of it.
But it's really not "happily ever after."
You've got two individuals with major traumatic events in their pasts. Both of them are sure to have trust issues - Sayu, likely easily frightened of anyone who tries to touch her, and Matsuda, likely afraid to trust anyone fully anymore, considering how much he looked up to Light for years and how badly that trust was shattered at the end of the series. Not to mention, the fact that Sayu is a Yagami surely incites some mixed feelings - likely, there would be times when Matsuda would look at her and everything would come flooding back. Likewise, to Sayu, Matsuda would be a reminder of the case that ended up killing her father and brother.
That actually sounds horrendous. So why put them together?
Angst is delicious Closure. The best way to overcome a fear is to conquer it head-on. Sayu may even find out that her brother was Kira - horrible to hear, of course, but it's a missing piece to the puzzle.
Picture this scenario: Sayu, having seen that she was being traded for a book, having heard her father say that he's not fit to be in the police because he valued his daughter over the most deadly weapon in history... how would any of that make sense? And there's nothing saying that she wouldn't be able to put two and two together, noting the coincidence between the fall of Kira and her brother's death. It's not pretty, but should she ever pry the information from Matsuda's lips, it would answer so many unanswered questions. It's a step towards moving on. Not to mention, being close with Matsuda - someone who is still positive and cheerful for the most part even after having been affected by the Kira case - has to be a sort of inspiration.
And as for Matsuda, he'd be happier knowing that no, he actually didn't screw that family over... and while anime!Matsuda may never know that he didn't actually kill Light, he can at least know that Sayu and Sachiko are pulling through okay, and that Sayu has gotten better - things have gotten better for them and he's a part of it. And with situations like theirs, it really is important to have someone who can fully understand what the other went through - I don't think anyone who wasn't directly affected by the Kira case could relate very easily to anyone that was. Matsuda especially needs someone who believes Kira was evil; sadly, that may be hard to find, looking in the general population.
...I told you it was horrifically speculative. Needless to say, if it happens, it couldn't happen for several years after the series, to give Sayu time to recover. And maybe I'm no different than Matsuda, quick to assume Light's actions are motivated by love.
But this is fandom. And it's fun. ...And honestly, Matsuda just deserves to finally be a part of that family.