It really depends upon context.
What one might say when someone wants to pre-order a book coming out next month (one form of contract), would be different that what one would say presenting a partnership agreement or a lease or a business joint venture agreement, or an employment agreement, or a real estate purchase agreement. Both the nature of the agreement and the character of the other party would be relevant.
Due to the "parol evidence rule" nothing said will be admissible in court anyway if it is an unambiguous "integrated" agreement which means it has an "entire agreement" clause.
In general, whenever two parties agree on the same terms with an intent to be bound, that will be binding in the absence of fraud in the inducement, duress, or a few other quite extreme limitations that aren't serious concerns unless the counter-parties have diminished capacity for some reason (e.g. you are presenting a contract to them in a language that they don't understand or are for some other reason, obviously very unsophisticated or vulnerable). No special warning or preface is required, although depending upon context, this may be customary.
Marital agreements are subject to special rules and so are agreements between people in a confidential or fiduciary relationship (like an attorney and a client). In these special relationships there is a legal requirement not just of consent, but of informed consent to a transaction that is substantively fair, and to a lack of undue pressure from the other party rather than a mere lack of legal duress. This is partially why your attorney was so careful to preface his or her statements to you in way that wouldn't normally be expected.
Sometimes, it is important to make clear that your offer is available for only a limited period of time, after which it is automatically withdrawn, or that your offer may be withdrawn at will and is not irrevocable, or that your offer may only be accepted by an action such as tendering a full or partial payment, or that you are not really making an offer at all and are instead soliciting requests from them to make an offer that will be considered if they return a signed document.