Yes, I've heard of others having the same issue.
Logos or no logos isn't the issue and is often misunderstood. Any part that Apple has a patent, copyright or IP rights to could be sized in customs and Apple pretty much files IP docs for anything that it designs (or even make a concept of) to protect their future interest with competition.
Most have seen the news in the past year about Apple suing Samsung over multi-touch functionality. An LCD screen that has this functionality even if it's the OS that does the major muscle. I'm not saying this is the specific reason because I wouldn't bet $1 that Apple doesn't have maybe 50 potential IP rights to some aspect of the screens that were seized.
The logo misunderstanding is simply avoiding the most obvious of Apple's IP rights; their Brand. One aspect that Customs officials have a fairly easy understanding of (and the manpower to enforce when they can)
Just because this one element is removed doesn't mean they can't enforce others. Foreign screen suppliers and buyers have simply been lucky up to this point not have had more sized as it's really Apple's influence to Customs as to when and what to snag as customs simply doesn't have the knowledge or manpower to stop everything.
Blackberry back in the day really put the heat on Customs and seizures were more likely to happen than not. RIM (Blackberry) also legally brought action against everyone from small ebay or repair shops up to large distribution organizations.
Just for reference, even if the screens were 100% OEM brand new, it would still be "illegal" to import them. You have to have a letter of license to import Apple branded product and without this any such parts or phones would be in violation. So many argue this with me because they've imported them for years with no issues. That doesn't change the facts and doesn't mean Apple or Customs won't decide to randomly seize shipments from time to time to shake things up.
So in reference to your second question, yes it's probably illegal to import even aftermarket parts for iPhone if:
A) Apple has any IP rights to various aspects of the design, parts or functionality.
B) You do not have a letter of license from Apple to import (don't bother trying to get one)
C) You are not an authorized distributor, manufacture, re seller or retailer of Apple parts.
You have a couple of options:
1) Ask customs to return the shipment. I see this happen often if you follow up and stay on top of things after customs sits around for several weeks. Side note: A college of mine had $250,000 of Moto V3 RAZR phones sized because they had aftermarket logo parts on them but after 6-7 years they released them). Of course, the value was about $10,000 by then. I've also talked to a parts supplier this year who had $50,000 worth of logo material sized but was ultimately returned to the shipper.
2) Try again - They probably only sized 1% (if that). Just have to potentially consider your company/address or supplier could now be on the radar. Some change the address and names of supplier/recipient.
3) Order from suppliers within your country. Remember, the main legality behind this is the act of importing. If you're not importing them then you're at least not violating this law. You may have to pay more but when evaluating the potential loss of a shipment in dollars and time to your business, it may be worth it.
My company buys back cracked glass LCD screens from repair shops and it seems this is starting to happen more and more lately. Still a small ratio but more so to know that someone behind the scenes is starting to pay attention. Why? No one exactly knows....If I were Apple I would do it once in a while to see the quality of aftermarket or refurbished OEM parts. I wouldn't want inferior stuff going back onto my brands devices because ultimately the consumer will have some negative view on Apple and not solely on the repair shop.
CEO of Harvest Cellular