I CAN run faster, but I'm heart rate training!!

So this evening I did session 2, week 1, of my 5 week heart rate program. The first two minutes was warmup, so I was supposed to keep a heart rate of about 50-60%. Fine. Then I was supposed to run for 25 minutes with a heart rate of 65-70%. When I run at my normal pace my heart rate is 80-85%. So to stay below 70% I had to plod along slower than an arthritic grandma - it was embarassing! I'm thinking about printing a t-shirt for my HR sessions which says both at the front and back "I can run faster really, but I'm heart rate training!". I hope it has some effect despite me barely breaking a sweat. I guess what it means is that I'm not very fit, otherwise my heart rate wouldnt be that high at such gentle exercise? 

It might be a good thing tho - I don't want to be too stiff for yoga tomorrow...