Aside from that being overly charitable to both Lopez and Urquiza...by my reading, say rather that Urquiza displays treachery and guile, and initially allows Lopez's forces to transit his territory as Paraguay demanded. He'll sucker punch Lopez in late 1863 or early 1864, depending on how long he can keep his nationalism under control. When the dust settles, Argentina absorbs all of Paraguay and possibly Uruguay as well, depending on how exhuasted Brazil is (and thus willing to accept cash instead of land).
Argentina, recall, has not yet acknowledged either Uruguay or Paraguay in 1861 as legitimate nations, and insists on calling them Argentine provinces in rebellion. Any "deal", or even respectful communication, between Argentina and one of those nations is a deception. Lopez is trickable, though. Urquiza doesn't want to fight Brazil (they look big), not even with Lopez as a distraction, particularly not with so little for him to gain (with Lopez as an extremely ambitious ally, nominally supporting Uruguayan sovereignty, the only thing Urquiza can possibly get from Brazil is cash. And there's only so much cash to be had.)