Yuna and David had a valid concern when asking about Ilya's past promiscuity, because they need to know that their son's partner is taking it seriously
The "I have only been in love with one person" line from Ilya is beautiful and poignant and said without doubt or hesitation, to relieve all of the Hollanders concerns.
But what I think is important is that Shane's response of "Same here. Only one." Though this may seem unnecessary to his parents ("we know you pretty well, Shane"), it's NOT unnecessary to Ilya.
Ilya crashed the fuck out over Rose Landry. Ilya expected Shane to bring Rose to All Star Weekend, in the books Ilya even expects Shane's "can I tell you something?" To be an engagement announcement. Rose could be open and affectionate with Shane in front of the whole world. The whole world thought that Rose and Shane were in love.
Ilya isn't used to being loved. Ilya doesn't believe he can be loved.
Ilya needed to know that not only does Shane love him, but at no point, regardless of how much Shane denied himself or how hard he tried with others, at NO POINT did he ever give his heart to anyone else.