Might well be - but that would mean history would record the existence of an additional starship named Enterprise
. And we get quite a few dialogue references to the number of starships named Enterprise
, and there's never room for an additional one that Pike would have flown.
If anything, we would prefer there to have been fewer Enterprises
than Kirk's, Harriman's, Garrett's and Picard's, so that these dialogue references could accommodate Archer's starship, too. But at least there we can say that Archer was a foreigner who did not serve in the UFP Starfleet and that his ship belonged to a foreign power, even though she indeed was a starship of the specified name. (Which incidentally means that there could have been plenty of starships of that name before NX-01, too, if the stories one day so require.)
I guess the statement suggests various alien species serving on that vessel, too, and not just "men" or human "people"
Semantically, I guess Pike isn't really concerned that he is responsible for these people (the way they comb their hair, they way they do their jobs), but specifically that he is responsible for these people's lives
- whether they die or not. The dramatic choice of words would be dictated by that already.
Anyway, if he's only concerned about lives, he's excluding all those sapient computers so faithfully serving aboard his ship!