Well, very simplistically, yes it is correct and should be expected to reduce headcount post-acquisition, that is the GCSE ('grade school') business studies answer: there are core functions which are non-linear in business growth if you like; that have an 'absolute' requirement but without a marginal need to grow as fast as the rest of the company. Thus an acquired company that is well-integrated doesn't need its payroll department any more, say.

And you don't buy out a company entirely because you like the way it's running(^) and just want all the profits for yourself. You buy it as a company because you think you have some kind of 'synergy' with it, or as an individual because you think you have better ideas for it; in either case you have some change to make that makes it worth more than it's present market valuation. It would be weird for an acquisition to result in no change.

(^So you like everything except think the dividend should be higher, I suppose.)