Yes, The relationship between sodium intake and hypertension is extremely well studied.
Does sodium intake affect hypertension?
Double-blind study of three sodium intakes and long-term effects of sodium restriction in essential hypertension.
20 patients with mild hypertension (average supine blood pressure without treatment, 164/101 mm Hg) reduced their salt intake to 50 mmol (3 g) per day for a month. They then entered a 3 month double-blind randomised crossover study of three levels of sodium intake: 200, 100, and 50 mmol per day. Blood pressure was significantly reduced on the middle and lowest sodium intakes. The average fall in blood pressure from the highest to the lowest sodium intake was 16/9 mm Hg. Patients continued to restrict their sodium intake for a further year. In 16 of the 20 patients blood pressure remained well controlled with salt restriction alone. Supine blood pressure at 1 year was 142/87 (SE 3/2) mm Hg with a 24 h urinary sodium excretion of 54 (7) mmol. These results show a progressive blood pressure fall as salt intake is reduced and that, in many patients with mild essential hypertension, blood pressure can be controlled without the need for drug therapy.
More recent examples confirming the correlation:
(these are the first four results I got on scholar.google.com key words: [sodium intake hypertension] 2011 or more recent. The fifth result was specific to Chinese adults so I stopped there.)
Over time, higher sodium intake is associated with increases in SUA and UAE. Among individuals with higher SUA and urine UAE, a higher sodium intake is an independent risk factor for developing hypertension.
(2014)(correspondence, specifically deals with some of the recent "confusion" that the question refers to. I don't feel that I am qualified enough to interpret any further but I recommend looking at it.)
After the IOM report was released, the TOHP data showed a direct, progressive relationship between lower sodium intake (down to intake below 1500 mg per day) and lower cardiovascular risk and there was no indication of a J-shaped curve
Sodium intake is positively associated with SBP and risk for pre-HBP/HPB among US children and adolescents, and this association may be stronger among those who are overweight/obese.
High quality evidence in non-acutely ill adults shows that reduced sodium intake reduces blood pressure and has no adverse effect on blood lipids, catecholamine levels, or renal function, and moderate quality evidence in children shows that a reduction in sodium intake reduces blood pressure. Lower sodium intake is also associated with a reduced risk of stroke and fatal coronary heart disease in adults. The totality of evidence suggests that most people will likely benefit from reducing sodium intake.
So, is this just for hypertensive individuals or everyone?
In another study "Effects on blood pressure of reduced dietary sodium and the Dietary Approaches to Stop Hypertension (DASH) diet"
participants ate foods with high, intermediate,
and low levels of sodium for 30 consecutive days
each, in random order.
of sodium were observed in participants with
and in those without hypertension, blacks and those of
other races, and women and men.
compared with the control diet with a high sodium
level, the DASH diet with a low sodium level led to a
mean systolic blood pressure that was 7.1 mm Hg
lower in participants without hypertension, and 11.5
mm Hg lower in participants with hypertension.
Finally, what's the association of heart disease with blood pressure?
Blood pressure, stroke, and coronary heart disease. Part 1, Prolonged differences in blood pressure: prospective observational studies corrected for the regression dilution bias. http://www.ncbi.nlm.nih.gov/pubmed/1969518
Within the range of DBP studied (about 70-110 mm Hg), there was no evidence of any "threshold" below which lower levels of DBP were not associated with lower risks of stroke and of CHD. ... prolonged differences in usual DBP of 5,7.5, and 10 mm Hg were respectively associated with at least 34%, 46%, and 56% less stroke and at least 21%. 29%, and 37% less CHD. ... The DBP results suggest that for the large majority of individuals, whether conventionally "hypertensive" or "normotensive", a lower blood pressure should eventually confer a lower risk of vascular disease.
This study was particularly focused on diastolic, so here are a couple that are concerned with systolic as well.
In conclusion, hypertensive and normotensive (all) people who cut back on their sodium(salt) intake should experience a lower (and thereby safer) blood pressure.