It should come as no surprise to you that I find that explanation illogical for a number of reasons. First, however, I'll note that I assume this line came because one of the Corinthians wised up for a moment and deigned to ask what I just asked, so kudos to that dude for using his head for a moment. Now, it's illogical for the following reasons:
a. If Jesus really had to have died, I'm sure god could have set him up in a sitch that would have had him killed, regardless if all of the Jews recognized his greatness. All things considered, in the end it was, indeed, the Romans that had him killed.
b. I mean, Jesus was apparently a common name at the time. Having a text that only has the name Jesus in it over and over would not be really helpful in identifying "the one true Jesus".
c. This point seems to absolve the Jews of blame for the death of Jesus, which is not really in line with the rest of the NT. Seems like Paul is trying to smooth things over with the Jewish members of the Corinth church. Had a non-Jewish church asked Paul this question, what would he have answered?