Is it possible for a liquid chemical to have a pH value lower than its aqueous solution? During the QC check of one of the products that we make as a company, the product had a $\mathrm{pH}$ of $10.44$ on one $\mathrm{pH}$ meter and $10.20$ on the other. (The product is a liquid, so it's straightforward to immerse $\mathrm{pH}$ probes to take the measurements.) 

For QC of the product, it is required to make a $1\%$ solution using demineralised water and to take a $\mathrm{pH}$ reading.

The first $\mathrm{pH}$ meter read $11.72$ for this $1\%$ solution, and the second meter read $11.41$.

How is it possible for the raw product's $\mathrm{pH}$ to be lower than the $1\%$ solution's $\mathrm{pH}$? The product is supposed to be basic and not acidic at all.
The concept of pH tends to break down when water is not greatly in excess of the solute (e.g. if your product is a highly concentrated amine base). The apparent pH of your product, when measured using a pH meter or an indicator, may be relatively low (seemingly less basic) if the solution has a less polar environment than that of pure water--because ionization will be less favorable.

If no water is present at all, the product might still give a pH reading with a meter or indicator, but the term "pH" in this case would be irrelevant.

It always helps to talk specifics with chemistry, so I am curious as to what the ingredients of the product are.