You are, of course, technically correct. It is conceivable that you could go back after the other party has spent the political capital to get iteration #1 through their parliament and tell them to rip it up and go for iteration #2, but if we’re dealing with even an iota of reality here, for any major treaty (which inevitably means stepping on toes, so you are using political capital), whether it’s trade, arms reduction, or environmental, there’s only a single kick at the can.
You can try and claim that you only sent it back for renegotiation, but let’s face it, if there’s a zero percent (to 2-3 decimal places) chance of the getting the other side to pass a a modified treaty, you’ve killed it. Better to call a spade a spade and stand up for what one believes in than pretend one is too stupid to understand the ramifications of one’s actions.