After a UK Family visit visa refusal, can I still enter the UK as a US citizen visa free or will I be refused at the border?

I recently applied for a UK Family Visit Visa but it got denied. We want to visit my husband parents long term but they said this:

You have applied for entry clearance to live in the UK indefinitely. As such, I am not satisfied that you genuinely intend a short visit only to the UK and that you will leave the UK at the end of the visit. Your application is refused under paragraphs V4.2(a) and (c) of Appendix V.

You state that you intend to work in the UK. Therefore I am not satisfied that you will not undertake any prohibited activities set out in V 4.5 – V 4.10. Your application has been refused under paragraph V4.2(d) and V4.5(a)

So our intention was to visit family and while visiting family apply for leave to remain status since we can only do it in the UK and not from the US. We thought we needed a visa to apply for that so when they asked us on our application if we are going to stay I said yes because my intentions in the future was to stay and work when if the leave to remain is granted. But I didn’t know it was a question for that visa I thought it was just a personal question.

Would if be bad if I told the border this if I got detained? Since I know they will ask me how and why I got denied and what were my intentions on this visit? I will have a return ticket just in case the leave to remain was not accepted and done in time so I’m not there living illegally.