Faldage, yours a very interesting point, and it comes down to defining precisely what is meant by "sexual" (as opposed to asexual) reproduction.
Concept-spinning here, and without any LIU, I would think the key point is that the DNA from two distinct individuals is combined, so that the offspring has DNA which each parent (individually) lacked, and thus brings together a new and potentially valuable combination of DNA. With asexual reproduction, the offspring would generally be a clone of its parent (except for mutations), thus minimizing the diversity from which natural selection (using that phrase in the biological sense) could select.
and yes, dr. bill, there are forms of asexual reproduction in which the offspring cell has only part, but not all, of the DNA of the parent cell, and hence is not a clone thereof. One example would be meiosis, the production of haploid cells from a diploid parent-cell.That is, I would thing that the test of whether reproduction is "sexual" would be whether genetic material so as to product a new combination -- regardless of how that new-combination cell then proceeds.
But I will say that bartleby provides no clear answer, as far as I can tell.
I'd think the test cannot be whether the genetic material combines (and/or the offspring develops) at a place
inside or a place
outside the body of a parent. For by that test, fish would be deemed asexual:
THE FISH
...
The chastest of the vertebrates,
He never even sees his mates,
but when they've finished, he appears
And O.K.'s all their bright ideas.
--- Ogden Nash
BTW, on the site on which I found this poem, it was immediately followed by Nashs poetic ode to the hippopotamus. Which see. 
btw #2: "O.K." is verbatim in the original.
