Admission cost for "seniors" to Royal Palace, Madrid?

If they didn't mean to restrict it, they wouldn't have that language on the website. That said, you never know what the person actually taking your money will say or do; front-line people sometimes don't like to fool with details, expecially when they are busy. If you plan to buy online tickets in advance, I highly recommend buying full-price tickets. Aside from the ethics of the situation, they'd be within their rights to void discounted tickets for which you do not qualify rather than just asking you to pay the difference.

Just follow the rules according to how you understand them as written in English and everyone will have peace before and when you get there.

We’ve been to many museums that have different prices for EU member countries’ citizens. Americans usually have to pay full price.

I notice Spain is specific in offering senior rates only to those who are 'local' (in their definition). There are some places that expand on it, but in general, assume full price. Now, they do allow tourist seniors (over 60) to travel on the train at a reduced rate once you have picked up your card in person.
Consider the Royal Palace on their free day. The Madrid Museums have free days or look at the combo museum card.

The Prado and Reina Sofia offer senior citizen discounts to Americans. All we had to do was show our passports.

And I would never go on a free day. The locals are not stupid and enjoy a free admission as much or more so than a cheap American tourist. We have found that free days are overwhelmingly crowded.

I've spent a lot of time in Spain over the last few years, and in my experience many tourist sights do not restrict senior discounts to EU citizens or Spanish citizens. The discounts available to me tended to be steeper than what I found in other western-European countries (often approaching 50%), so I felt very fortunate even though I sometimes did have to pay full price. The discounts are large enough that I was really sorry I was only 64-1/2 during my first trip. The savings are significant even if not offered to me everywhere.

Two years ago when purchasing tickets to the Royal Palace (for my father who was over 65), we were denied a discount as soon as they asked for ID and saw the American passport.

2 years ago in November, I was at the Royal Palace on free day and was allowed entrance. If they have changed policy, my apologies for old news...hmm, or I wonder if it was due to being Nov 9th which is Madrid's Patron Saint Day? I also decided to pay entry to Prado and Theissen museums and free entry to the Reina Sofia because of my limited interest. Sure, there were lots of local university students entering, but as I take a slower pace, they would just ebb and flow around me. I didn't have to wait long for plenty of breathing room for what I wanted to see.

I believe the limitation of EU citizens only for discounts has to do with reciprocity. We don’t give it, so we don’t get it. Some of what appears to be inconsistency has to do with the ownership or sponsorship of the site. That is, a privately owned attraction can set their own rules; but government owned ones will follow national or local policies set by the entity to which the site belongs.
While it is true that some gatekeepers are lax about enforcement, we found that more prevalent in Italy than in Spain. In Spain, we usually were given the discount with proof of age and no requirement regarding citizenship.
We have had one experience with free entry days - - at the Uffizi many years ago - - and have never wanted to repeat it. It was so crowded, that, being short, we could not see the paintings. As soon as one person stepped away from the row closest to a work, someone else stepped into the space. We were only able to get extreme side views.

" It was so crowded, that, being short, we could not see the paintings" @Roslyn, I almost made the comment that I, at 5'8" was fine but that short people may have a different experience. Your post reinforced it.

My wife attempted to get the senior discount at the Royal Palace in July but couldn’t get it with her American passport. If you are buying tickets on site it’s worth a try but I wouldn’t try it for an advanced purchase as you might have to buy an additional full price admission. She was able to get the discount at other sites in Spain.

Thanks to everyone for the feedback. I'd like to get tickets in advance and didn't want to miss out on a discounted price if it's available but I'll juts buy them at full price. I'm pleased with the discounts offered to those of us who are over 65 at many sights. When we traveled in Italy, they almost always gave us a discount even when we didn't ask for one. A penny saved....

Spain unlike Italy and France routinely offered senior discounts to all seniors when we were there a few years ago -- we did not encounter any that were restricted to locals -- but that may change. FWIW, I don't think in Schengen or the EU they are allowed to provide different rules to Spaniards and other EU residents. But they can certainly exclude American tourists as they do in Italy and France usually. (note that Europeans can avail themselves of such discounts everywhere in the US with the exception of some local transport which may only give senior rates with special senior cards for locals)