I disagree, strongly.
The right's discussed in the Bill of rights are pre-existing, as a function of being human. The BOR prohibits the government from taking away or restricting those preexisting rights of people.
There is no other right enumerated in the 1st ten ammendments that we feel only belongs to a citizen. Freedom of speech, freedom of religion, the right to be secure in your home and effects, have a fair trial and not incriminate yourself are all rights the government is prohibited from violating against any person. There is nothing in the second amendment to imply that it doesn't also enjoin the government from infringing on the rights of non citizens to go armed.
Further, the constitution separates citizen from person in several places.
No Person shall be a Representative who shall not have attained to the Age of twenty five Years, and been seven Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State in which he shall be chosen.
Clearly saying that a Citizen is a sub-set of Person (capitalization theirs). Person being singular of People. They do the same thing with requirement to be a Senator and POTUS.
Article IV also delineates a difference between Citizen and Person (or People):
The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.
A Person charged in any State with Treason, Felony, or other Crime, who shall flee from Justice, and be found in another State, shall on Demand of the executive Authority of the State from which he fled, be delivered up, to be removed to the State having Jurisdiction of the Crime.
Where the founders meant "Citizen" they said it. The Bill of Rights talks about "People" because it prohibits government abuse of everyone in the country.
Certainly folks have read it the wrong way in the past (slaves, freed slaves, and Indians being the obvious examples), but it's clear.
Also taken in concert with the Declaration of Independence that the Rights are conferred by the Creator upon all men, and the BOR prevents the government from abusing those Creator granted rights, the delineation between People and Citizen is even more nonsensical.
I too would like to see our immigration laws actually enforced. The folks here illegally should be arrested, given due process while respecting their human rights, and if found guilty of illegally entering the US, deported and flagged to deny further entry.