Today I received an email from longtime blog reader Elliot Miller inquiring about concedes that. I hadn’t previously encountered that usage, so of course I searched for it on the SEC’s EDGAR system. If you exclude its use in conditional clauses (If Acme concedes that …) and language of discretion (Acme may concede that …), where it plays a supporting role, concedes that is something of a rarity: I looked at 70 contracts on EDGAR that use “concedes” before I found the following example:
Debtor recognizes and concedes that non-judicial remedies are consistent with the usage of trade, are responsive to commercial necessity and are the result of a bargain at arm’s length.
In that context, concedes that serves the same function as acknowledges that (a form of language of declaration). Since you don’t want to use two different words to convey the same meaning, stick with acknowledges that. It has the benefit of being less in-your-face than asking the other guy to concede something.