According to several books written about Market-Garden campaign, including by Paratrooper Don Burgett 1/506th, and 101st Historian Mark Bando, there was fighting in Eindhoven. It was primarily carried out by 1st Battalion 506th, as well as by D Co, 2/506th.

I visited Eindhoven last year for the 71th of Market-Garden. A local guide took me around the 101st area of operations, starting in Eindhoven where he showed me the locations of several 88mm guns (also detailed in books by Burgett et al.) that were knocked out by paratroopers, as well as a church occupied by German snipers.

The Americans didn't exactly walk into Eindhoven, but at the same time there was nowhere near the same level of resistance offered like there was in Arnhem and Nijmegen.