It sounds like a marginal piece. Is one side dark, as if it was just below the bark? Does the piece maintain its 1.5" thickness from corner to corner? If not, it might be n/g. The effect of knots varies on structural members. First, it matters if the knots are tight and solid vs. large and loose. Also, it matters what kind of load the piece is under. You can double the strength of most stair strings by "sistering" a 2x4 or 6 near the bottom edge under the treads. If they do this for you then it will probably be strong enough. Also, the location of the knots can matter. This has largely been forgotten by modern builders. For weight bearing members, such as stringers and floor joists, the bottom edge is under tension and the top edge is under compression. Non-loose knots can be strong and fine under compression (top edge of member) but loose and/or large knots should not be at the bottom edge of a bearing member. This is similar to the codes regarding allowable holes being cut in joists for plumbing or electric runs. These must be kept a certain distance up from the bottom edge because it needs integrity because it is in tension. The location of a bottom edge knot along the length of a board also makes a difference. The end thirds of any spanned member has far less tension than the middle third. Be wary of large or loose knots near, or at the bottom of a weight bearing member, especially if in the middle third of its length.
If they don't agree to sister it below the treads then you should have someone look at it, maybe your local building inspector or your wife's friend's carpenter husband, etc.. It might be ok, with cosmetic problems or it might be totally no good. Can't tell positively from here.