What makes a compound basic?
Aluminum chlorohydrate (ACH) is a group of specific aluminum salts having the general formula $\ce{Al_nCl_{(3n-m)}(OH)_m}$ (Wikipedia). It is used in cosmetics as an antiperspirant and as a coagulant in water purification. Specifically in wastewater treatment processes, ACH is used as a coagulant to remove dissolved organic matter and colloidal particles present in suspension. In his paper on Water Treatment Coagulants, Peter Gebbie describes what coagulants do (Ref.1):


  With aluminium-based coagulants, the metal ion is hydrolyzed to form aluminium hydroxide floc as well as hydrogen ions. The hydrogen ions will react with the alkalinity of the water and in the process, decrease the pH of the water as can be seen from Equation [...].  Similarly for ACH, which is described as being a pre-hydrolyzed coagulant, the following reaction takes place: 
  $$\ce{Al2(OH)5Cl -&gt; Al2(OH)5+ + Cl- + H2O -&gt; 2Al(OH)3 + H+ + Cl- }$$
  Less hydrogen ions are produced with ACH, reflecting the hydroxylated nature of this compound.


There it says it all: ACH is more basic than other aluminum salts because it is pre-hydroxylated.

Aluminum chlorohydrate is one of the most common active ingredients in commercial antiperspirants. The variation most commonly used in deodorants and antiperspirants is $\ce{Al2Cl(OH)5}$, similar to the one used in water purification.

Note: Your statement of "The pH value of ACH is about 4" is evidently not correct. However, W. R. Grace &amp; Company (producer of solution form of ACH) listed solubility of ACH as $\pu{1000 g/L}$ at $\pu{20 ^\circ C}$ and $\mathrm{pH} = 3.3$, the optimum condition.

Reference:


Peter Gebbie, “An Operator’s Guide to Water Treatment Coagulants,” 31st Annual Water Industry Workshop – Operations Skills; University Central Queensland Campus: Rockhampton, Australia, 4 to 6 July, 2006, pp. 14–20 (http://wioa.org.au/conference_papers/06_qld/documents/PeterGebbie.pdf).